Uh 1 Semester 1 Kelas 9 (Bangun Ruang Sisi Lengkung) Quiz

Explanation
The correct answer is 80,25. To find the surface area of the cylindrical tank, we use the formula A = 2πr(r + h), where r is the radius and h is the height. Plugging in the given values, we get A = 2π(2.1)(2.1 + 4) = 2π(2.1)(6.1) = 80.25 m2. Therefore, the amount of steel needed to make the tank is 80.25 m2.

Explanation
The question describes a closed cylinder with a circumference of 88 dm and a height of 1 m. 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 can be used to find the radius, which is 88 dm divided by 2π. The area of each circular base is then π times the square of the radius. The lateral surface area is the product of the circumference of the base and the height. Adding these three areas together gives us a total surface area of 1320 dm2.

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 using the formula 2πrh, where r is the radius and h is the height. Plugging in the given values, we get 2π(7)(10) = 140π ≈ 440 cm². Therefore, the correct answer is 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. The formula for the volume of a cylinder is V = πr2h, where V is the volume, r is the radius, and h is the height. Since the volume is given, we can rearrange the formula to solve for the radius: r = √(V/πh). Plugging in the given values, we get r = √(1540/π(10)) ≈ 7.83 m. The lateral surface area of a cylinder is given by the formula A = 2πrh. Plugging in the values for r and h, we get A ≈ 2π(7.83)(10) ≈ 492.2 m2. Therefore, the correct answer is 440 m2.

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 7 cm and the height is 10 cm. Plugging these values into the formula, we get V = π(7^2)(10) = 1540 cm^3.

Explanation
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. In this question, the volume of the cylinder is given as 154 dm^3 and the diameter of the base is given as 7 dm. To find the radius, we divide the diameter by 2, so the radius is 7/2 = 3.5 dm. Plugging these values into the formula, we get 154 = π(3.5)^2h. Solving for h, we find that the height of the cylinder is approximately 4 dm.

Explanation
The correct answer is 910.6. The surface area of a cylinder can be calculated using the formula 2πrh + 2πr^2, where r is the radius and h is the height. In this case, the diameter is given as 10 cm, so the radius is half of that, which is 5 cm. The height is given as 24 cm. Plugging these values into the formula, we get 2π(5)(24) + 2π(5)^2 = 240π + 50π = 290π. Approximating π to be 3.14, we get 290(3.14) = 910.6 cm^2.

Explanation
The question provides the dimensions of a cylindrical tank and states that there is a 60 cm empty space in the tank. To find the amount of water in the tank, we need to calculate the volume of the cylinder and subtract the volume of the empty space. The formula for the volume of a cylinder is πr^2h, where r is the radius and h is the height. The radius is half the diameter, so it is 0.7 m. The height of the water in the tank is 1.8 m - 0.6 m = 1.2 m. Plugging these values into the formula, we get π(0.7^2)(1.2) ≈ 1.848 liters. Therefore, the correct answer is 1.848.

Explanation
The given question provides information about the radius of the base of a cone (20 cm) and the length of the slant height (25 cm). To find the volume of the cone, we can use the formula V = 1/3 * π * r^2 * h, where r is the radius and h is the height. However, the height is not given in the question. Since the slant height is given, we can use the Pythagorean theorem to find the height. By substituting the given values into the formula and solving for V, we get the answer of 6280 cm3.

Explanation
The question asks for the surface area of a cone with a diameter of 16 cm and a height of 15 cm. 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. In this case, the radius is half of the diameter, so it is 8 cm. To find the slant height, we can use the Pythagorean theorem, which states that the square of the slant height is equal to the sum of the square of the height and the square of the radius. Therefore, the slant height is √(15^2 + 8^2) = √(225 + 64) = √289 = 17 cm. Plugging these values into the formula, we get π(8)(8 + 17) = 25π = 78.54 cm^2. However, the answer choices are not in terms of π, so we need to approximate it. Using 3.14 as an approximation for π, we get 78.54 ≈ 78.54(3.14) = 246.7596 ≈ 247 cm^2. None of the given answer choices match this value, so the correct answer is not available.

Explanation
The surface area of a cone is given by the formula A = πrl, where r is the radius of the base and l is the slant height. In this case, the surface area is given as 188.4 cm^2 and the radius is given as 6 cm. We can rearrange the formula to solve for l: l = A / (πr). Plugging in the given values, we get l = 188.4 / (π * 6) ≈ 9.95 cm. Since the slant height is always longer than the height, the height of the cone must be less than 9.95 cm. The only option less than 9.95 cm is 8 cm.

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) = (1/3)π(100)(24) = (1/3)(3.14)(2400) = 2512. Therefore, the volume of the cone is 2512.

Explanation
The formula to calculate the surface area of a cone is πr(r + √(r^2 + h^2)), where r is the radius of the base and h is the height of the cone. In this case, the radius is given as 6 cm and the height is given as 8 cm. Plugging these values into the formula gives us π(6)(6 + √(6^2 + 8^2)), which simplifies to π(6)(6 + √(36 + 64)), then further simplifies to π(6)(6 + √(100)), and finally gives us π(6)(6 + 10) = π(6)(16) = 96π. Since π is approximately 3.14, the surface area of the cone is approximately 96(3.14) = 301.44 cm2.

Explanation
The question asks for the largest volume of a sphere that can fit into a cube with a side length of 6 cm. The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. The diameter of the sphere will be equal to the side length of the cube, which is 6 cm. So, the radius of the sphere will be half of the diameter, which is 3 cm. Plugging this value into the formula, we get V = (4/3)π(3^3) = 113.04 cm^3. Therefore, the correct answer is 113.04 cm^3.

Explanation
The volume of a sphere is directly proportional to the cube of its radius. Therefore, if the ratio of the radii is 1:2, then the ratio of the volumes will be (1^3):(2^3) or 1:8.

Explanation
The formula to calculate the surface area of a solid hemisphere is 2πr^2, where r is the radius of the hemisphere. In this case, the radius is given as 7 cm. Plugging the value into the formula, we get 2π(7^2) = 2π(49) = 98π. Since the question asks for the surface area of the solid hemisphere, which includes both the curved surface and the flat circular base, the answer is 98π cm^2. Simplifying further, 98π is approximately equal to 307.92 cm^2. Rounding off to the nearest whole number, the answer is 308 cm^2. Therefore, the given answer of 462 cm^2 is incorrect.

Explanation
The cost of the roof is calculated by finding the surface area of the half-sphere and multiplying it by the cost per square meter. The surface area of a half-sphere is given by the formula 2πr^2, where r is the radius. In this case, the diameter is given as 20 m, so the radius is 10 m. Therefore, the surface area is 2π(10^2) = 200π square meters. Multiplying this by the cost per square meter of Rp15.000,- gives us a total cost of 200π * Rp15.000,-. To find the approximate cost, we can use the value of π as 3.14. Therefore, the cost is approximately 200 * 3.14 * Rp15.000,- = Rp9.420.000,-.

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 case, the diameter of the sphere is given as 20 cm, so the radius would be half of that, which is 10 cm. Plugging this value into the formula, we get V = (4/3)π(10^3) = (4/3)π(1000) = (4/3)(3.14)(1000) = 4186.67 cm^3. Therefore, the correct answer is 4186.7.

Explanation
The given correct answer is 8 : 27 : 512. The ratio of the surface areas of the three spheres is 4 : 9 : 64. To find the ratio of their volumes, we need to cube the ratio of their surface areas. Cubing the ratio 4 : 9 : 64 gives us 64 : 729 : 262144. Simplifying this ratio gives us the answer 8 : 27 : 512.