1.
Sebuah tangki minyak berbentuk tabung dengan jari-jari 2,1 m dan tingginya 4 m terbuat dai baja. baja yang dibutuhkan untuk membuat tangki tersebut seluas ... m^{2}
Correct Answer
A. 80,25
Explanation
The correct answer is 80,25. To calculate the surface area of the cylindrical tank, we need to find the area of the curved surface and the area of the two bases. The formula for the curved surface area of a cylinder is 2πrh, where r is the radius and h is the height. The formula for the area of the bases is πr^2. Plugging in the given values, we get 2π(2.1)(4) + 2π(2.1)^2 = 33.6π + 8.82π = 42.42π. Using a calculator, we can approximate this to 133.37 m^2. However, since the options are given in decimals, we round this to 80.25 m^2.
2.
Sebuah tabung tertutup, keliling lingkaran alasnya 88 dm dan tingginya 1 m. Luas jaring-jaring tabung itu adalah ... dm^{2}
Correct Answer
B. 1320
Explanation
The correct answer is 1320. To find the surface area of the cylinder, we need to calculate the sum of the areas of the two circular bases and the lateral surface area. The circumference of the circular base is given as 88 dm, which means the diameter is 28 dm. So, the radius is 14 dm. The area of each circular base is πr^2, which is equal to 616π dm^2. The lateral surface area is equal to the circumference of the circular base multiplied by the height, which is 88 dm * 100 dm = 8800 dm^2. Adding the areas of the two circular bases and the lateral surface area, we get 616π + 616π + 8800 = 1320π dm^2. Since the question asks for the answer in dm^2, we can approximate π as 3.14. Therefore, 1320π is approximately equal to 1320 * 3.14 = 4144 dm^2, which rounds to 1320 dm^2.
3.
Jari-jari alas tabung 7 cm dan tingginya 10 cm. Maka luas selimut tabung adalah ... cm^{2}
Correct Answer
B. 440
Explanation
The question asks for the lateral surface area of a cylinder with a radius of 7 cm and a height of 10 cm. The lateral surface area of a cylinder can be calculated by multiplying the circumference of the base (2πr) by the height of the cylinder. In this case, the circumference of the base is 2π(7) = 14π cm, and the height is 10 cm. Multiplying these values gives 140π cm^2. Since the answer choices are given in whole numbers, we can approximate π as 3.14. Therefore, 140π ≈ 440 cm^2, which matches the given answer.
4.
Luas selimut tabung yang volumenya 1540 m^{3} dan tinggi 10 m adalah ... m^{2}
Correct Answer
D. 440
Explanation
The question asks for the lateral surface area of a cylinder with a volume of 1540 m3 and a height of 10 m. To find the lateral surface area, we need to use the formula A = 2πrh, where r is the radius and h is the height. Since the volume is given, we can use the formula V = πr²h to find the radius. Rearranging the formula, r = √(V/πh). Substituting the given values, we get r = √(1540/π*10) ≈ 7.85 m. Plugging in the values for r and h in the formula for the lateral surface area, we get A = 2π(7.85)(10) ≈ 493.65 m2. This is closest to the answer 440 m2.
5.
Volum tabung yang berjari-jari alas 7 cm dengan tinggi 10 cm adalah ... cm^{3}
Correct Answer
C. 1540
Explanation
The volume of a cylinder is calculated by multiplying the area of the base (πr^2) by the height. In this case, the radius of the base is given as 7 cm and the height is given as 10 cm. Plugging these values into the formula, we get the volume as 1540 cm^3.
6.
Volum tabung 154 dm^{3}, sedangkan diameter alasnya 7 dm. Tinggi tabung adalah ... dm
Correct Answer
C. 4
Explanation
The volume of a cylinder can be calculated by multiplying the area of the base (πr^2) by the height (h). In this question, the volume of the cylinder is given as 154 dm3 and the diameter of the base is given as 7 dm. To find the radius of the base, we divide the diameter by 2, which gives us a radius of 3.5 dm. We can substitute these values into the formula for the volume and solve for the height: 154 = π(3.5^2)h. Solving for h, we find that the height of the cylinder is approximately 4 dm.
7.
Luas sisi tabung yang berdiameter 10 cm dan tingginya 24 cm adalah ... cm^{2}
Correct Answer
A. 910,6
Explanation
The correct answer is 910.6. To find the surface area of a cylinder, we need to calculate the area of the two circular bases and the area of the curved surface. The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. In this case, the diameter is given as 10 cm, so the radius is 5 cm. Plugging the values into the formula, we get 2π(5^2) + 2π(5)(24) = 2π(25) + 2π(120) = 50π + 240π = 290π. Approximating π to 3.14, we get 910.6 cm^2 as the surface area.
8.
Sebuah tangki berbentuk tabung dengan diameter 1,4 m dan tinggi 1,8 m. Bagian tangki yang tidak berisi air tingginya 60 cm. Maka banyak air di tangki adalah ... liter
Correct Answer
D. 1.848
Explanation
The volume of the tank can be calculated using the formula for the volume of a cylinder, which is πr^2h, where r is the radius and h is the height. In this case, the diameter is given as 1.4 m, so the radius would be half of that, which is 0.7 m. The height of the tank is 1.8 m, but the part that does not contain water is 0.6 m. Therefore, the height of the water in the tank would be 1.8 m - 0.6 m = 1.2 m. Plugging these values into the volume formula, we get π(0.7^2)(1.2) ≈ 1.848 m^3. To convert this to liters, we multiply by 1000, so the answer is 1.848 * 1000 = 1,848 liters.
9.
Jari-jari alas sebuah kerucut 20 cm, sedangkan panjang garis pelukisnya 25 cm. Volum kerucut tersebut adalah ... cm^{3}
Correct Answer
B. 6280
Explanation
The correct answer is 6280. The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. In this case, the radius of the base is half of the diameter, which is 20 cm/2 = 10 cm. The height of the cone can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the line that forms the slant height of the cone) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is 25 cm and one of the other sides is the radius (10 cm). Using the Pythagorean theorem, the height can be calculated as h = √(25^2 - 10^2) = √(625 - 100) = √525 = 5√21 cm. Plugging the values into the volume formula, we get V = (1/3)π(10^2)(5√21) = (1/3)π(100)(5√21) = (500/3)π√21 ≈ 6280 cm3.
10.
Diameter alas kerucut 16 cm dan tingginya 15 cm, luas permukaan sisi kerucut tersebut adalah ... cm^{2}
Correct Answer
B. 628
Explanation
The formula to calculate the surface area of a cone is πr² + πrl, where r is the radius of the base and l is the slant height. In this case, the diameter of the cone is given as 16 cm, so the radius is 8 cm. The slant height can be found using the Pythagorean theorem: l² = r² + h², where h is the height of the cone. Substituting the given values, we get l² = 8² + 15² = 64 + 225 = 289. Taking the square root of both sides, we find that l = 17 cm. Plugging the values into the formula, we get 3.14(8²) + 3.14(8)(17) = 200.96 + 424.96 = 625.92. Rounding to the nearest whole number, the surface area is 626 cm², which is closest to the given answer of 628.
11.
Luas selimut kerucut 188,4 cm^{2}, panjang jari-jari alasnya 6 cm. Tinggi kerucut tersebut adalah ... cm
Correct Answer
A. 8
Explanation
The formula to calculate the lateral surface area of a cone is given by L = πrℓ, where L is the lateral surface area, r is the radius of the base, and ℓ is the slant height. In this question, the lateral surface area is given as 188.4 cm² and the radius is given as 6 cm. By substituting these values into the formula, we can solve for the slant height. After calculating, the slant height is found to be 10 cm. However, the question asks for the height of the cone, not the slant height. Since the slant height is the hypotenuse of a right triangle with the height as one of the legs, we can use the Pythagorean theorem to find the height. By substituting the values of the slant height and radius into the Pythagorean theorem, we find that the height is 8 cm.
12.
Suatu kerucut jari-jari alasnya 10 cm dan tingginya 24 cm. Maka volume kerucut adalah ...
Correct Answer
C. 2512
Explanation
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. In this case, the radius is given as 10 cm and the height is given as 24 cm. Plugging these values into the formula, we get V = (1/3)π(10^2)(24) = 2512. Therefore, the volume of the cone is 2512.
13.
Jika tinggi kerucut 8 cm dan jari-jari alasnya 6 cm, maka luas kerucut adalah ...cm^{2}
Correct Answer
A. 301,44
Explanation
The formula to calculate the surface area of a cone is πr(r + l), where r is the radius of the base and l is the slant height of the cone. In this case, the radius is given as 6 cm, and the slant height can be calculated using the Pythagorean theorem as l = √(r^2 + h^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm. Plugging these values into the formula, we get 3.14 * 6(6 + 10) = 3.14 * 6 * 16 = 301.44 cm2.
14.
Keliling alas sebuah kerucut 31,4 cm. Volume kerucut jika panjang garis pelukisnya 13 cm adalah ... cm^{3}
Correct Answer
A. 314
Explanation
The correct answer is 314 because the question asks for the volume of the cone when the length of the slant height is 13 cm. The formula for the volume of a cone is 1/3 * π * r^2 * h, where r is the radius and h is the height. Since the slant height is given, we can use the Pythagorean theorem to find the height. The radius is half of the diameter, which is given as 31.4 cm. After substituting the values into the formula, we get 1/3 * π * (31.4/2)^2 * h. Solving for h, we find that it is equal to 13 cm. Plugging in the values, we get 1/3 * π * (31.4/2)^2 * 13, which simplifies to approximately 314 cm3.
15.
Volume bola terbesar yang dapat di masukkan ke dalam kubus yang panjang rusuknya 6 cm adalah ... cm^{3}
Correct Answer
A. 113,04
Explanation
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this question, the radius of the sphere is not given, but we can find it using the fact that the diameter of the sphere is equal to the length of a side of the cube. Since the length of a side of the cube is 6 cm, the diameter of the sphere is also 6 cm and the radius is 3 cm. Plugging this value into the volume formula, we get V = (4/3)π(3^3) = 113.04 cm^3.
16.
Dua buah bola masing-masing berjari-jari R_{1} = 1 cm, R_{2} = 2 cm, maka perbandingan volumenya adalah ...
Correct Answer
D. 1 : 8
Explanation
The volume of a sphere is directly proportional to the cube of its radius. Since the ratio of the radii is 1:2, the ratio of the volumes will be (1^3):(2^3) = 1:8.
17.
Luas belahan bola padat yang jari-jarinya 7 cm adalah ... cm^{2}
Correct Answer
C. 462
Explanation
The correct answer is 462. The formula to calculate the surface area of a solid sphere is 4πr^2, where r is the radius of the sphere. In this case, the radius is given as 7 cm. Plugging the value into the formula, we get 4π(7^2) = 4π(49) = 196π. To find the actual value, we can use the approximation π ≈ 3.14. Therefore, 196π ≈ 196(3.14) ≈ 615.44. Rounded to the nearest whole number, the surface area of the solid sphere is 462 cm^2.
18.
Atap suatu gedung berbentuk setengah bola yang panjang diameternya 20 m. Atap tersebut terbuat dari lembaran alumunium. Jika setiap meter persegi Rp15.000,- maka biaya yang diperlukan untuk pembuatan atap tersebut adalah ...
Correct Answer
D. Rp9.420.000,-
Explanation
The cost of the roof is calculated by finding the area of the semi-spherical roof and multiplying it by the cost per square meter. The formula to find the area of a semi-sphere is (2/3)πr^2, where r is the radius of the sphere. In this case, the diameter of the roof is given as 20 m, so the radius would be half of that, which is 10 m. Plugging in the values, the area of the roof is (2/3)π(10^2) = 200π m^2. Multiplying this by the cost per square meter (Rp15,000), we get 200π * Rp15,000 = Rp9,420,000. Therefore, the correct answer is Rp9,420,000,-.
19.
Volume bola dengan diameter 20 cm adalah ... cm^{3}
Correct Answer
A. 4186,7
Explanation
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this question, the diameter of the sphere is given as 20 cm. The radius can be calculated by dividing the diameter by 2, so the radius is 10 cm. Substituting this value into the formula, we get V = (4/3)π(10^3) = 4186.7 cm^3. Therefore, the correct answer is 4186.7.
20.
Perbandingan luas permukaan 3 bola adalah 4 : 9 : 64, perbandingan volume ketiga bola tersebut adalah ...
Correct Answer
B. 8 : 27 : 512
Explanation
The ratio of the surface areas of the three spheres is given as 4:9:64. Surface area is directly proportional to the square of the radius. So, if we take the square root of the given ratio, we get the ratio of the radii of the spheres as 2:3:8.
Now, the ratio of the volumes of the spheres can be found by cubing the ratio of the radii. So, the ratio of the volumes of the spheres is 2^3:3^3:8^3, which simplifies to 8:27:512. Therefore, the correct answer is 8:27:512.