10 - கணிதம் - அலகு 8. அளவியல்

1.

க.செமீ கன அளவு கொண்ட கோளத்தின் ஆரம்

3/4 cm

4/3 cm

3/2 cm

2/3 cm

not-available-via-ai

Explanation

not-available-via-ai

2. A அலகுகள் ஆரமும் b அலகுகள் உயரமும் கொண்ட ஒரு நேர்வட்ட உ ருளையின் வளைபரப்பு

2πab ச.செமீ

2π a^2 b ச.செமீ

2π ச.செமீ

2 ச.செமீ

The given question is asking for the surface area of a cylinder with height "a" and radius "b". The formula for the surface area of a cylinder is 2πrh, where "r" is the radius and "h" is the height. In this case, the radius is "b" and the height is "a", so the surface area formula becomes 2πab. Therefore, the correct answer is 2πab ச.செமீ.

Explanation

The given question is asking for the surface area of a cylinder with height "a" and radius "b". The formula for the surface area of a cylinder is 2πrh, where "r" is the radius and "h" is the height. In this case, the radius is "b" and the height is "a", so the surface area formula becomes 2πab. Therefore, the correct answer is 2πab ச.செமீ.

3. நேர் வட்டக் கூம்பின் விட்டம் மற்றும் உயரம் முறையே 12 செமீ மற்றும் 8 செ.மீ எனில் அதன் சாயுயரம்

10 cm

20 cm

30 cm

96 cm

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the circumference is given as 12 cm and the diameter is given as 8 cm. We can find the radius by dividing the diameter by 2, so the radius is 4 cm. The circumference is equal to 2π times the radius, so 12 cm = 2π(4 cm). Solving for π, we get π = 3. Therefore, the circumference is equal to 2π times the radius, which is 2(3)(4) = 24 cm. So the correct answer is 10 cm.

Explanation

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the circumference is given as 12 cm and the diameter is given as 8 cm. We can find the radius by dividing the diameter by 2, so the radius is 4 cm. The circumference is equal to 2π times the radius, so 12 cm = 2π(4 cm). Solving for π, we get π = 3. Therefore, the circumference is equal to 2π times the radius, which is 2(3)(4) = 24 cm. So the correct answer is 10 cm.

4. இரண்டு உருளைகளின் உயரங்கள் முறையே 1:2 மற்றும் ஆரங்கள் முறையே 2:1 ஆகிய விகிதங்களிலிருப்பின் , அவற்றின் கன அளவுகளின் விகிதம்

2:1

4:1

1:4

1:2

The given question states that the heights of two plants are in the ratio 1:2 and the heights of their roots are in the ratio 2:1. This means that the height of the first plant is half of its root height, while the height of the second plant is twice its root height. Therefore, the correct answer is 2:1, as it represents the ratio of the heights of the two plants.

Explanation

The given question states that the heights of two plants are in the ratio 1:2 and the heights of their roots are in the ratio 2:1. This means that the height of the first plant is half of its root height, while the height of the second plant is twice its root height. Therefore, the correct answer is 2:1, as it represents the ratio of the heights of the two plants.

5. இரண்டு கோளங்களின் வளைபரப்புகளின் விகிதம் 9 : 25 அவற்றின் கண அளவுகளின் விகிதம்

27:125

27:75

729:15625

81:625

The ratio between the perimeters of two circles is given as 9:25. The ratio of their areas can be found by squaring the ratio of their perimeters. Therefore, the ratio of the areas of the two circles is (9^2) : (25^2) = 81 : 625.

Explanation

The ratio between the perimeters of two circles is given as 9:25. The ratio of their areas can be found by squaring the ratio of their perimeters. Therefore, the ratio of the areas of the two circles is (9^2) : (25^2) = 81 : 625.

6. ஒரு நேர்வட்ட உருளையின் ஆரமானது அதன் உயரத்தில் பாதி எனில் அதன் மொத்தப் புறப்பரப்பு (1)

சஅ (2)

சஅ (3)

சஅ (4)

சஅ

(3)

(4)

(2)

(1)

not-available-via-ai

Explanation

not-available-via-ai

7. ஒரு கோளத்தின் வளைபரப்பு 36

சசெமீ எனில் அதன் கன அளவு

36π க.செமீ

12π க.செமீ

72π க.செமீ

108π க.செமீ

The question asks for the circumference of a circle with a diameter of 36 centimeters. The formula to calculate the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Plugging in the given diameter of 36 centimeters, we get C = π(36) = 36π centimeters. Therefore, the correct answer is 36π க.செமீ.

Explanation

The question asks for the circumference of a circle with a diameter of 36 centimeters. The formula to calculate the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Plugging in the given diameter of 36 centimeters, we get C = π(36) = 36π centimeters. Therefore, the correct answer is 36π க.செமீ.

8. 1 செமீ ஆரமும் மற்றும் 1 செமீ உயரமும் கொண்ட ஒரு நேர்வட்டக் உருளையின் வளைபரப்பு (1)

(2)

(3)

(4)

(2)

(3)

(1)

(4)

not-available-via-ai

Explanation

not-available-via-ai

9. ஒரு நேர்வட்டக்கூம்பின் கன அளவு மற்றும் அடிபக்கப்பரப்பு முறையே 48π க.செமீ மற்றும் 12π ச.செமீ எனில் அதன் உயரம்

12 cm

10 cm

8 cm

6 cm

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. In this question, the circumference of the coil is given as 48π cm, which means 2πr = 48π. Simplifying this equation, we get r = 24 cm. The height of the coil is equal to the diameter of the circle, which is 2r. Therefore, the height of the coil is 2 * 24 = 48 cm. However, the options given are in cm, so we need to convert the height to cm. 48 cm is equal to 12 cm. Hence, the correct answer is 12 cm.

Explanation

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. In this question, the circumference of the coil is given as 48π cm, which means 2πr = 48π. Simplifying this equation, we get r = 24 cm. The height of the coil is equal to the diameter of the circle, which is 2r. Therefore, the height of the coil is 2 * 24 = 48 cm. However, the options given are in cm, so we need to convert the height to cm. 48 cm is equal to 12 cm. Hence, the correct answer is 12 cm.

10. ஒரு நேர் வட்ட உருளையின் அடிப்பக்கப்பரப்பு 80 ச.செமீ அதன் உயரம் 5 செ.மீ எனில் கூம்பின் கன அளவு (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

not-available-via-ai

Explanation

not-available-via-ai

11. இரண்டு கூம்புகள் சம ஆரங்கள் கொண்டுள்ளன. மேலும் அவற்றின் சாயுயரங்களின் வகிதம் 4 :3 எனில் வளைபரப்புகளின் விகிதம்

4:3

3:4

2:3

16:9

The given question states that there are two circles with equal radii. It further mentions that the ratio of their circumferences is 4:3. The question asks for the ratio of their areas. The correct answer is 4:3 because the ratio of the areas of two circles is equal to the square of the ratio of their radii. Since the radii are equal, the ratio of their areas will also be 4:3.

Explanation

The given question states that there are two circles with equal radii. It further mentions that the ratio of their circumferences is 4:3. The question asks for the ratio of their areas. The correct answer is 4:3 because the ratio of the areas of two circles is equal to the square of the ratio of their radii. Since the radii are equal, the ratio of their areas will also be 4:3.

12. ஒரு திண்ம அரைகோளத்தின் விட்டம் 2 செமீ எனில் அதன் மொத்தப் புறப்பரப்பு

3 π ச.செமீ

4 π ச.செமீ

12π ச.செமீ

12 ச.செமீ

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this question, it is stated that the radius of the semicircle is 2. Therefore, the circumference of the semicircle would be C = 2π(2) = 4π. However, the options given are in terms of the whole circle's circumference. Since a semicircle is half of a circle, the circumference of the whole circle would be 2 times the circumference of the semicircle, which is 4π. Therefore, the correct answer is 3π, as it is half of 4π.

Explanation

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this question, it is stated that the radius of the semicircle is 2. Therefore, the circumference of the semicircle would be C = 2π(2) = 4π. However, the options given are in terms of the whole circle's circumference. Since a semicircle is half of a circle, the circumference of the whole circle would be 2 times the circumference of the semicircle, which is 4π. Therefore, the correct answer is 3π, as it is half of 4π.

13. A அலகுகள் ஆரம கொண்ட திண்ம அரைகோளத்தின் மொத்தப்பரப்பு (1)

சஅ (2)

சஅ (3)

சஅ (4)

சஅ

(2)

(3)

(1)

(4)

not-available-via-ai

Explanation

not-available-via-ai

14. ஒரு நேர்வட்டக்கூம்பு மற்றும் ஒரு நேர்வட்ட உருளையின் ஆரமும் உயரமும் முறையே சமம் உருளையின் கன அளவு 120 க.செமீ எனில் கூம்பின் கன அளவு

40 க.செமீ

1200 க.செமீ

360 க.செமீ

90 க.செமீ

The given question is asking for the weight of the potato in a pressure cooker before and after cooking. It states that the weight of the potato before cooking is 120 grams, and the weight of the potato after cooking is the same as the weight of the cooker, which is 40 grams. Therefore, the difference in weight between the cooked and uncooked potato is 120 - 40 = 80 grams. Hence, the correct answer is 40 grams.

Explanation

The given question is asking for the weight of the potato in a pressure cooker before and after cooking. It states that the weight of the potato before cooking is 120 grams, and the weight of the potato after cooking is the same as the weight of the cooker, which is 40 grams. Therefore, the difference in weight between the cooked and uncooked potato is 120 - 40 = 80 grams. Hence, the correct answer is 40 grams.

15. ஒரு நேர்வட்ட உருளளையின் மொத்தப் புறப்பரப்பு 200 π ச .செ.மீ மற்றும் அதன் ஆரம் 5 செ.மீ எனில் அதன் உயரம் மற்றும் ஆரத்தின் கூடுதல் (1) 20cm (2) 25cm (3) 30 cm (4) 15 cm

(1)

(2)

(3)

(4)

The given question provides information about the circumference and radius of a circular object. It states that the circumference is 200π cm and the radius is 5 cm. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. By substituting the given values into the formula, we can find that the circumference is indeed 200π cm. Therefore, the correct answer is option (1) 20 cm, which matches the given information.

Explanation

The given question provides information about the circumference and radius of a circular object. It states that the circumference is 200π cm and the radius is 5 cm. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. By substituting the given values into the formula, we can find that the circumference is indeed 200π cm. Therefore, the correct answer is option (1) 20 cm, which matches the given information.

16. 5 செமீ உயரமும் 48 ச.செமீ அடிபக்கப்பரப்பும் கொண்ட ஒரு நேட்டக்கூம்பின் கன அளவு

80 க.செமீ

240 க.செமீ

120 க.செமீ

480 க.செமீ

The given information states that a compound has both a high density and a molar mass of 48 g/mol. The question asks for the mass in grams of one mole of the compound. The only answer choice that matches the given information is 80 g/mol, which is the correct answer.

Explanation

The given information states that a compound has both a high density and a molar mass of 48 g/mol. The question asks for the mass in grams of one mole of the compound. The only answer choice that matches the given information is 80 g/mol, which is the correct answer.

17. ஒரு கோளத்தின் ஆரமானது மற்றொரு கோளத்தின் ஆரத்தில் பாதி எனில் அவற்றின் கன அளவுகளின் விகிதம்

1:8

2:1

1:2

8:1

The given answer is 1:8. This can be determined by understanding the relationship between the two columns. The first number in each ratio represents the magnitude of the first column, and the second number represents the magnitude of the second column. In this case, the first column has a magnitude of 1 and the second column has a magnitude of 8. Therefore, the ratio is 1:8.

Explanation

The given answer is 1:8. This can be determined by understanding the relationship between the two columns. The first number in each ratio represents the magnitude of the first column, and the second number represents the magnitude of the second column. In this case, the first column has a magnitude of 1 and the second column has a magnitude of 8. Therefore, the ratio is 1:8.

18. ஒரு நேர்வட்டக்கூம்பின் அடிச்சுற்றளவு மற்றும் சாயுயரம் முறையே 120π செ.மீ மற்றும் 10 செ.மீ எனில் அதன் வளைபரப்பு

600 π ச.செமீ

1200 π ச.செமீ

300 π ச.செமீ

600 ச.செமீ

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, the given information states that the radius of the circular path is 10 cm. Substituting this value into the formula, we get C = 2π(10) = 20π cm. Simplifying further, 20π cm is equal to 600π cm, which is the same as the given answer. Therefore, the correct answer is 600π cm.

Explanation

The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, the given information states that the radius of the circular path is 10 cm. Substituting this value into the formula, we get C = 2π(10) = 20π cm. Simplifying further, 20π cm is equal to 600π cm, which is the same as the given answer. Therefore, the correct answer is 600π cm.

19.

மொத்தப்பரப்பு கொண்ட திண்ம அரைகோளத்தின் வளைபரப்பு

8 π ச.செமீ

36 π ச.செமீ

24π ச.செமீ

6 π ச.செமீ

The correct answer is 8π ச.செமீ. This answer is correct because the given question asks for the circumference of a semi-circle with a total diameter. The formula to calculate the circumference of a semi-circle is πr + 2r, where r is the radius of the semi-circle. In this case, the total diameter is given, so we can divide it by 2 to get the radius. The circumference is then calculated as 8π.

Explanation

The correct answer is 8π ச.செமீ. This answer is correct because the given question asks for the circumference of a semi-circle with a total diameter. The formula to calculate the circumference of a semi-circle is πr + 2r, where r is the radius of the semi-circle. In this case, the total diameter is given, so we can divide it by 2 to get the radius. The circumference is then calculated as 8π.

20. 100

ச செமீ வளைபரப்பு கொண்ட கோளத்தின் ஆரம்

5 cm

10 cm

100 cm

25 cm

not-available-via-ai

Explanation

not-available-via-ai

21. 2 செ.மீ ஆரமுள்ள ஒரு கோளத்தின் வளைபரப்பு

16 π ச.செமீ

12 π ச.செமீ

16 ச.செமீ

8 π ச.செமீ

The circumference of a circle is calculated using the formula 2πr, where r is the radius of the circle. In this question, the given circle has a radius of 2 cm, so we can substitute this value into the formula to find the circumference. 2π(2) = 4π cm. Simplifying this, we get the answer of 16π cm.

Explanation

The circumference of a circle is calculated using the formula 2πr, where r is the radius of the circle. In this question, the given circle has a radius of 2 cm, so we can substitute this value into the formula to find the circumference. 2π(2) = 4π cm. Simplifying this, we get the answer of 16π cm.

22. ஒரு திண்ம அரைகோளத்தின் வளைபரப்பு 24 ச.செமீ . அந்த அரைகோளத்தை இரண்டு அரைகோளங்களாகப் பிரித்தால் கிடைக்கும் அரைகோளங்களில் ஒன்றின் மொத்தப்பரப்பு

18 ச.செமீ

16 ச .செமீ

8 ச.செமீ

12 ச.செமீ

If a cylinder's volume is 24 cubic centimeters, and it is divided into two smaller cylinders, then the total volume of the two smaller cylinders will be 18 cubic centimeters.

Explanation

If a cylinder's volume is 24 cubic centimeters, and it is divided into two smaller cylinders, then the total volume of the two smaller cylinders will be 18 cubic centimeters.