1. Which formula represents the volume of a cylinder?
Answer:
Explanation:
The volume of a cylinder is given by the product of its base area (πr^2) and its height (h).
2. The surface area of a cube with side length 'a' is:
Answer:
Explanation:
A cube has 6 equal sides, each with an area of a^2. So, the total surface area is 6 times a^2.
3. Which of the following shapes has the same formula for volume and surface area?
Answer:
Explanation:
A cube's volume is a^3 and its surface area is 6a^2. Although the formulas are different, both are derived from the side length 'a'.
4. The formula for the volume of a cone is:
Answer:
Explanation:
The volume of a cone is one-third the product of its base area (πr^2) and its height (h).
5. Which of the following is NOT a curved surface?
Answer:
Explanation:
A cube is made up of flat surfaces, while the other options have at least one curved surface.
6. The curved surface area of a cylinder is given by:
Answer:
Explanation:
The curved surface area of a cylinder is the product of the circumference of its base (2πr) and its height (h).
7. If the radius of a sphere is doubled, its surface area will:
Answer:
Explanation:
The surface area of a sphere is 4πr^2. If the radius is doubled, the surface area becomes 4π(2r)^2 which is 4 times the original.
8. The volume of a sphere with radius 'r' is:
Answer:
Explanation:
The volume of a sphere is given by (4/3) times π times the cube of its radius.
9. Which shape has the least surface area for a given volume?
Answer:
Explanation:
Among all shapes with the same volume, a sphere has the least surface area.
10. The height of a cylinder is 10 cm and its volume is 100π cm^3. What is its radius?
Answer:
Explanation:
Using the formula for the volume of a cylinder, πr^2h = 100π. With h = 10 cm, r^2 = 10, so r = 2 cm.
11. If the surface area of a cube is 54 cm^2, its volume is:
Answer:
Explanation:
The side of the cube is sqrt(54/6) = 3 cm. Therefore, its volume is 3^3 = 27 cm^3.
12. A cuboid turns into a cube when:
Answer:
Explanation:
A cuboid becomes a cube when all its dimensions are the same.
13. The ratio of the volume of two similar spheres with radii r and 2r is:
Answer:
Explanation:
The volume of a sphere is proportional to the cube of its radius. Thus, the ratio becomes r^3:(2r)^3 = 1:8.
14. The total surface area of a hemisphere of radius 'r' is:
Answer:
Explanation:
The total surface area includes the curved surface area (2πr^2) and the flat circular part (πr^2), totaling 3πr^2.
15. The volume of a frustum (a cone with the top cut off) is calculated using the:
Answer:
Explanation:
The volume of a frustum is given by (1/3)πh(r1^2 + r2^2 + r1*r2), where r1 and r2 are the radii of the two ends.
16. The volume of a pyramid is:
Answer:
Explanation:
The volume of a pyramid is one-third the product of its base area and its height.
17. Which of the following shapes has no edges?
Answer:
Explanation:
A sphere is a smooth, round object with no edges.
18. The diagonal of a cuboid is calculated using:
Answer:
Explanation:
The diagonal of a cuboid can be found using the Pythagoras' theorem in three dimensions.
19. The ratio of the volumes of two similar cylinders with heights h and 2h is:
Answer:
Explanation:
The volume of a cylinder is proportional to the square of its radius and its height. Thus, the ratio becomes h^2:h^2*2^2 = 1:4.
20. The lateral surface area of a cone excludes:
Answer:
Explanation:
The lateral surface area of a cone refers to only the curved surface, not its base.