1. The height, radius, and slant height of a right circular cone always form the three sides of a right-angled triangle.

2. The height, radius, and slant height of a right circular cone always form the three sides of a right-angled triangle.

3. "The height, radius, and slant height of a right circular cone always form the three sides of a right-angled triangle."

4. 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

5. 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

6. 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

7. 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

8. Two solid spheres with radii of 8 cm and 10 cm are melted to form a right circular cone with a height of 42 cm. What is the radius of the cone?

(a) 8 cm (b) 10 cm (c) 12 cm (d) 16 cm

9. If a right circular cone has a height of \(12\) cm and a volume of \(1024\pi\) cubic cm, what is the slant height of the cone?

(a) 20 cm (b) 21 cm (c) 22 cm (d) 23 cm

10. If the three sides of a triangle are in the ratio 5 : 12 : 13, then the triangle will always be a right-angled triangle.

11. A right circular cone has a height of 12 cm and a volume of \(100\pi\) cubic cm. Find the slant height of the cone.

12. 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.

13. Perfectly explained. The triangle formed is a right-angled isosceles triangle, where the angle of elevation is 45°, making the opposite and adjacent sides equal. So, the height of the pillar equals the distance from its base: 20 meters.

(a) 1:2:3 (b) 1:5:7 (c) 1:7:9 (d) None of the above

14. If \(h\), \(s\), and \(v\) represent the height, curved surface area, and volume of a right circular cone respectively, then the value of \(3πVh^3 – s^2h^2 + 9V^2\).

(a) 16\(\pi\) (b) 0 (c) 4\(\pi\) (d) 32\(\pi^2\)

15. If a right circular cone has a radius of \(\frac{r}{2}\) units and a slant height of \(2l\) units, then the total surface area is \(2πr(r + l)\).

16. A right circular cone has a slant height of 7 cm and a total surface area of 147.84 cm². Find the radius of the base of the cone.

17. If the slant height of a right circular cone is 15 cm and the diameter of its base is 16 cm, then the lateral surface area of the cone is –

(a) \(60\pi\) square cm (b) \(68\pi\) square cm (c) \(120\pi\) square cm (d) \(130\pi\) square cm

18. If the volume of a right circular cone is \(100\pi\) cubic cm and its height is 12 cm, find the slant height of the cone.

19. Find the radius of the base of a right circular cone whose slant height is 7 cm and total surface area is 147.84 cm².

20. A solid right circular cone is melted to form a solid right circular cylinder of the same radius, with a height of \(5\) cm. Determine the height of the cone.

(a) 10 cm (b) 15 cm (c) 18cm (d) 24cm

21. Find the radius of the base of a right circular cone if its slant height is 7 cm and its total surface area is 147.84 cm².

22. 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.

23. A right circular cylinder with the same radius and height has a volume that is three times the volume of a right circular cone.

24. A solid right circular cone is melted to form a solid cylinder of the same radius, with a height of 5 cm. Find the height of the cone.

25. The lateral surface area of a right circular cone with a base radius of 1.5 meters and a slant height of 14 meters is _____.

(a) 66 square meters (b) 22 square meters (c) 44 square meters (d) 88 square meters

26. The lateral surface area of a right circular cone with a base radius of 1.5 meters and a slant height of 14 meters is _____.

(a) 66 square meters (b) 22 square meters (c) 44 square meters (d) 88 square meters

27. Determine the radius of the base of a solid right circular cone with a slant height of 7 cm and a total surface area of 147.84 square cm.

28. 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

29. The slant height of a right circular cone is 7 cm, and the total surface area is 147.84 cm². Determine the radius of its base.

30. The slant height of a right circular cone is 7 cm, and its total surface area is 147.84 square cm. Find the radius of its base.