Soal Matematika Smp Ix : Bangun Ruang Sisi Lengkung

1. Pernyataan tentang tabung berikut yang benar adalah . . ...

mempunyai 3 buah rusuk

mempunyai 2 bidang sisi

bidang alas dan bidang atas berupa daerah lingkaran yang sejajar dan kongruen

panjang jari-jari lingkaran atas kurang dari panjang jari-jari lingkaran alas

The correct answer is that the cylinder has a base and a top that are parallel and congruent circular regions. This means that the base and top of the cylinder are both circular and have the same size and shape. They are also parallel to each other, which means that they lie in the same plane and do not intersect. This is a characteristic of a cylinder, as it has two circular faces that are parallel and congruent to each other.

Explanation

The correct answer is that the cylinder has a base and a top that are parallel and congruent circular regions. This means that the base and top of the cylinder are both circular and have the same size and shape. They are also parallel to each other, which means that they lie in the same plane and do not intersect. This is a characteristic of a cylinder, as it has two circular faces that are parallel and congruent to each other.

2. Volume tabung yang ukuran diameternya 10 cm, tinggi 8 cm, dan π = 3,14 adalah .. .cm³

721

628

586

436

The volume of a cylinder can be calculated using the formula V = πr^2h, 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 (10 cm / 2). The height is given as 8 cm. Plugging these values into the formula, we get V = 3.14 * 5^2 * 8 = 628 cm^3.

Explanation

The volume of a cylinder can be calculated using the formula V = πr^2h, 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 (10 cm / 2). The height is given as 8 cm. Plugging these values into the formula, we get V = 3.14 * 5^2 * 8 = 628 cm^3.

3. Luas selimut tabung yang panjang diameter alasnya 46 cm dan tinggi 7 cm adalah . . . .cm²

1.412

1.012

1.000

942

The correct answer is 1.012. The formula to calculate the lateral surface area of a cylinder is 2πrh, where r is the radius of the base and h is the height. In this case, the diameter of the base is given as 46 cm, so the radius would be half of that, which is 23 cm. The height is given as 7 cm. Plugging these values into the formula, we get 2π(23)(7) = 322π ≈ 1012. Hence, the lateral surface area of the cylinder is approximately 1.012 cm2.

Explanation

The correct answer is 1.012. The formula to calculate the lateral surface area of a cylinder is 2πrh, where r is the radius of the base and h is the height. In this case, the diameter of the base is given as 46 cm, so the radius would be half of that, which is 23 cm. The height is given as 7 cm. Plugging these values into the formula, we get 2π(23)(7) = 322π ≈ 1012. Hence, the lateral surface area of the cylinder is approximately 1.012 cm2.

4. Sebuah kerucut diameternya 18 cm dan tingginya 10 cm (π= 3,14). Volume kerucut = ... cm³

384

643,8

791,4

847,8

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius and h is the height. In this case, the diameter of the cone is given as 18 cm, so the radius would be half of that, which is 9 cm. The height is given as 10 cm. Plugging these values into the formula, we get V = (1/3)π(9²)(10) = 847.8 cm³. Therefore, the correct answer is 847.8.

Explanation

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius and h is the height. In this case, the diameter of the cone is given as 18 cm, so the radius would be half of that, which is 9 cm. The height is given as 10 cm. Plugging these values into the formula, we get V = (1/3)π(9²)(10) = 847.8 cm³. Therefore, the correct answer is 847.8.

5. Diketahui luas selimut sebuah tabung adalah 2.200 cm². Jik tinggi tabung 25 cm dan π = 22/7, maka luas permukaan tabung itu adalah . . . .cm²

3432

3234

2239

2214

The surface area of a cylinder consists of two parts: the area of the two bases and the area of the curved surface. The formula for the surface area of a cylinder is 2πr(r+h), where r is the radius of the base and h is the height of the cylinder. In this question, the height of the cylinder is given as 25 cm, and the formula for the surface area can be simplified to 2πrh. Given that the curved surface area is 2200 cm2, we can substitute the values into the formula and solve for the radius. After finding the radius, we can plug it back into the formula to calculate the total surface area, which is 3432 cm2.

Explanation

The surface area of a cylinder consists of two parts: the area of the two bases and the area of the curved surface. The formula for the surface area of a cylinder is 2πr(r+h), where r is the radius of the base and h is the height of the cylinder. In this question, the height of the cylinder is given as 25 cm, and the formula for the surface area can be simplified to 2πrh. Given that the curved surface area is 2200 cm2, we can substitute the values into the formula and solve for the radius. After finding the radius, we can plug it back into the formula to calculate the total surface area, which is 3432 cm2.

6. Suatu kerucut dibentuk dari selembar aluminium yang berbentuk setengah lingkaran dengan diameter 42 cm. Untuk π = 22/7, maka panjang jari-jari lingkaran alas kerucut adalah ... cm

8,6

10

10,5

11,6

The diameter of the semicircle is given as 42 cm. The formula to find the radius of a circle from its diameter is r = d/2. Therefore, the radius of the semicircle is 42/2 = 21 cm. Since the semicircle is the base of the cone, the radius of the base of the cone is also 21 cm.

Explanation

The diameter of the semicircle is given as 42 cm. The formula to find the radius of a circle from its diameter is r = d/2. Therefore, the radius of the semicircle is 42/2 = 21 cm. Since the semicircle is the base of the cone, the radius of the base of the cone is also 21 cm.

7. Keliling alas sebuah tabung adalah 24 cm dan tinggi tabung 15 cm. Untuk π = 22/7, maka luas selimut tabung tersebut adalah ... cm²

230,45

360

423,20

575

The formula to calculate the lateral surface area of a cylinder is 2πrh, where r is the radius of the base and h is the height of the cylinder. Given that the circumference of the base (keliling alas) is 24 cm, we can calculate the radius by dividing the circumference by 2π. So, the radius is 24/(2*22/7) = 24/44 = 12/22 = 6/11 cm. The height of the cylinder is given as 15 cm. Plugging these values into the formula, we get 2*(22/7)*(6/11)*(15) = 360 cm2.

Explanation

The formula to calculate the lateral surface area of a cylinder is 2πrh, where r is the radius of the base and h is the height of the cylinder. Given that the circumference of the base (keliling alas) is 24 cm, we can calculate the radius by dividing the circumference by 2π. So, the radius is 24/(2*22/7) = 24/44 = 12/22 = 6/11 cm. The height of the cylinder is given as 15 cm. Plugging these values into the formula, we get 2*(22/7)*(6/11)*(15) = 360 cm2.

8. Ditentukan kerucut dengan tinggi 8 cm dan jari-jari alasnya 6 cm. Untuk π = 3,14, maka luas seluruh permukaan kerucut tersebut adalah . ... cm²

301,44

188,40

113,04

100,48

The surface area of a cone is given by the formula A = πr(r + l), where r is the radius of the base and l is the slant height. In this case, the radius is 6 cm and the slant height can be found using the Pythagorean theorem: l = √(r^2 + h^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm. Plugging these values into the formula, we get A = 3.14(6(6 + 10)) = 3.14(6(16)) = 3.14(96) = 301.44 cm2.

Explanation

The surface area of a cone is given by the formula A = πr(r + l), where r is the radius of the base and l is the slant height. In this case, the radius is 6 cm and the slant height can be found using the Pythagorean theorem: l = √(r^2 + h^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm. Plugging these values into the formula, we get A = 3.14(6(6 + 10)) = 3.14(6(16)) = 3.14(96) = 301.44 cm2.

9. Sebuah bola besi dimasukkan ke dalam tabung yang penuh berisi air. Jari-jari tabung sama dengan jari-jari bola, yaitu 10 cm. Sedangkan tinggi tabung 19 cm. Jika π = 3,14, maka sisa air di dalam tabung sesudah bola dimasukkan adalah . ... cm³

3.380,70

2.742

1.797,33

1.779,33

When the iron ball is inserted into the cylinder, it displaces an amount of water equal to its own volume. 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 case, the radius of the sphere is 10 cm, so the volume of the sphere is (4/3)π(10^3) = 4,188.79 cm^3. Therefore, the amount of water displaced is 4,188.79 cm^3. Since the cylinder is already full with water, the remaining water in the cylinder after the ball is inserted is equal to the volume of the cylinder minus the volume of the ball, which is 19π(10^2) - 4,188.79 = 3,380.70 cm^3.

Explanation

When the iron ball is inserted into the cylinder, it displaces an amount of water equal to its own volume. 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 case, the radius of the sphere is 10 cm, so the volume of the sphere is (4/3)π(10^3) = 4,188.79 cm^3. Therefore, the amount of water displaced is 4,188.79 cm^3. Since the cylinder is already full with water, the remaining water in the cylinder after the ball is inserted is equal to the volume of the cylinder minus the volume of the ball, which is 19π(10^2) - 4,188.79 = 3,380.70 cm^3.

10. Sebuah bola dimasukkan ke dalam tabung. Diameter bola sama dengan diameter tabung, yaitu 12 cm, tinggi tabung 20 cm, dan π = 3,14. Volume tabung di luar bola adalah . ... cm³

523,33

657,17

1.226,08

1.356,48

The volume of the cylinder can be calculated using the formula V = πr^2h, where r is the radius of the cylinder and h is the height. Since the diameter of the cylinder and the ball is the same, the radius of the cylinder is half of the diameter, which is 6 cm. Therefore, the volume of the cylinder is 3.14 * 6^2 * 20 = 2260.8 cm^3.
The volume of the ball can be calculated using the formula V = (4/3)πr^3, where r is the radius of the ball. Since the diameter of the ball is 12 cm, the radius is 6 cm. Therefore, the volume of the ball is (4/3) * 3.14 * 6^3 = 904.32 cm^3.
The volume of the space outside the ball in the cylinder can be calculated by subtracting the volume of the ball from the volume of the cylinder: 2260.8 - 904.32 = 1356.48 cm^3.
Therefore, the correct answer is 1,356.48 cm^3.

Explanation

The volume of the cylinder can be calculated using the formula V = πr^2h, where r is the radius of the cylinder and h is the height. Since the diameter of the cylinder and the ball is the same, the radius of the cylinder is half of the diameter, which is 6 cm. Therefore, the volume of the cylinder is 3.14 * 6^2 * 20 = 2260.8 cm^3.
The volume of the ball can be calculated using the formula V = (4/3)πr^3, where r is the radius of the ball. Since the diameter of the ball is 12 cm, the radius is 6 cm. Therefore, the volume of the ball is (4/3) * 3.14 * 6^3 = 904.32 cm^3.
The volume of the space outside the ball in the cylinder can be calculated by subtracting the volume of the ball from the volume of the cylinder: 2260.8 - 904.32 = 1356.48 cm^3.
Therefore, the correct answer is 1,356.48 cm^3.