1. The shape of a one-end sharpened pencil is a combination of a cone and a **cylinder**.
2. The shape of a one-end-sharpened pencil is a combination of a cylinder and a cone.
3. The shape of a one-ended sharpened pencil is a combination of a cone and a __________.
4. The shape of a sharpened pencil is a combination of a cone and a _____.
5. The shape of a pencil is a combination of a cone and a ___.
6. The shape of a single-cut pencil is a combination of a cone and _____.
7. If the ratio of the radii of two perpendicular solid cones is 2:3 and the ratio of their heights is 5:3, what is the ratio of their volumes ?
(a) 27:20 (b) 20:27 (c) 4:9 (d) 9:4
8. There is some water in a vertical cylindrical drum. Three solid right circular cone-shaped iron pieces, each having a base diameter of 32 cm and height of 40 cm, are completely submerged in the water. As a result, the water level in the drum rises by 12.8 cm. Find the diameter of the drum.
9. A tent in the shape of a right elliptical cone has a base area of 13.86 square meters. The tent requires a tarpaulin worth 5775 rupees for construction, and the cost of one square meter of tarpaulin is 150 rupees. Determine the height of the tent and the volume of air it can hold in liters.
10. The mountain is in the shape of a right circular cone. Its slant height is 2.5 km, and its base area is 1.54 square km. Determine the height of the mountain.
11. A solid object has its lower part in the shape of a hemisphere and its upper part in the shape of a right circular cone. If the surface areas of both parts are equal, determine the ratio of the radius to the height of the cone.
12. A vertical circular cylindrical vessel with a diameter of 24 cm contains some water. If 60 solid cone-shaped iron pieces, each with a base diameter of 6 cm and height of 4 cm, are fully submerged in the water, calculate and write how much the water level will rise.
13. The bottom part of a solid is in the shape of a hemisphere, and the top part is in the shape of a right circular cone. If the surface areas of both parts are equal, then calculate and write the ratio of the radius to the height of the cone.
14. To make a right circular cone-shaped tent, 77 square meters of canvas was used. If the slant height of the tent is 7 meters, then calculate and write the area of the base of the tent.
15. The lower part of an ice cream is conical in shape, and the upper part is hemispherical, both having the same base. If the height of the cone is 9 cm and the radius of the base is 2.5 cm, calculate the volume of the ice cream.
16. A solid sphere has a total surface area of 1386 cm². It is melted and reshaped into several right circular cones, each with a radius of 3.5 cm and a height of 6 cm. Find the radius of the solid sphere and determine how many such cones are formed.
17. If the base radius of a right circular cone is 3 cm and the height is 4 cm, then the lateral surface area of the cone will be.
(a) \(10\pi \, cm^2\) (b) \(15\pi \, cm^2\) (c) \(12\pi \, cm^2\) (d) \(18\pi \, cm^2\)
18. The volume of a right circular cone is V. If both the height and the radius are doubled, the new volume will be:
(a) 3V (b) 4V (c) 6V (d) 8V
19. If the radius of a right circular cone is \(\cfrac{r}{2}\) units and the slant height is \(2l\) units, then the total surface area is –
(a) \(2πr (l+r)\) square units (b) \(πr\left(l+\cfrac{r}{4}\right)\) square units (c) \(πr(l+r)\) square units (d) \(2πr l\) square units
20. If the volumes of two cones are in the ratio 1:4 and the ratio of the diameters of their bases is 4:5, find the ratio of their heights
(a) 1:5 (b) 5:4 (c) 5:16 (d) 25:64
21. If a hemisphere and a cone have equal base areas and equal heights, then what will be the ratio of their volumes?
(a) 1:3 (b) 2:3 (c) 3:2 (d) 3:1
22. If a cone has a base diameter of 12 cm and an apex angle of 60°, what is its height?
(a) \(2\sqrt3\) cm (b) \(6\) cm (c) \(6\sqrt3\) cm (d) None of the above
23. If a right circular cone and a sphere have the same radius, and the numerical value of the cone's volume is equal to the numerical value of the sphere's curved surface area, then what is the height of the cone?
(a) 10 units (b) 11 units (c) 12 units (d) 13 units
24. The ratio of the base radii of two right circular cones is 2 : 3, and the ratio of their heights is 3 : 2. Then the ratio of their volumes is —
(a) 3:2 (b) 9:4 (c) 4:9 (d) 2:3
25. If a right circular cone has a base diameter of 7 cm and a slant height of 10 cm, what is the total surface area of the cone?
(a) 184.5 square cm (b) 185.4 square cm (c) 148.5 square cm (d) 184.6 square cm
26. What is the ratio of the volumes of a right circular cylinder and a cone having the same radius and height?
(a) 1:3 (b) 3:2 (c) 3:1 (d) 2:3
27. A right circular cone has a base radius of 20 cm and a height of 10 cm. If it is melted down, how many solid spheres of radius 2 cm can be made from it?
(a) 200 (b) 100 (c) 250 (d) 125
28. If the base area of a right circular cone is \(A\), its height is \(H\), and its volume is \(V\), then express \(H\) in terms of \(V\) and \(A\).
(a) \(H=\cfrac{3V}{A}\) (b) \(H=\cfrac{V}{A}\) (c) \(H=\cfrac{V}{3A}\) (d) \(H=\cfrac{3V}{2A}\)
29. If the diameters of two cones are equal and the ratio of their slant heights is 5:7, then what is the ratio of their curved surface areas?
(a) 25:7 (b) 25:49 (c) 5:49 (d) 5:7
30. If the volume of a right circular cone is \(100\pi\) cubic centimeters and its height is 12 cm, then what is its slant height?
(a) 13 cm (b) 16 cm (c) 9 cm (d) 26 cm
