1. 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

2. 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 \(2πr(r + l)\).

3. The base radius of a solid right circular cone is \(r\) units, its vertical height is \(h\) units, and its slant height is \(l\) units. The cone’s base is attached to the base of a solid right circular cylinder. If the base radius and height of the cylinder are equal to those of the cone, then the total surface area of the combined solid is \((πrl + 2πrh + 2πr^2)\) square units.

4. If the radius of a tall circular cone is \( \frac{r}{2} \) units and the slant height is \( 2l \) units, then find the total surface area of the cone.

(a) \(2πr(l+r)\) square units (b) \(πr(l+\cfrac{r}{4})\) square units (c) \(πr(l+r)\) square units (d) \(2πrl\) square units

5. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and curved surface area will be equal.

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

12. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

13. 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 the base and the area of the base of the cone. Let me know if you'd like the full solution worked out as well. I'm happy to help.

14. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and its curved surface area will be equal.

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

16. If the slant height of a right circular cone is 7 cm and its total surface area is 147.84 square cm, then find the diameter of the cone.

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. 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

19. 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

20. If the radius of a cone is \(r\) units, the height is \(h\) units, and the curved surface area is \(S\) square units, then prove that \[ h = \frac{\sqrt{S^2 - \pi^2 r^4}}{\pi r} \]

21. The volume of a right circular cone is \(V\) cubic units. If the area of the base is \(A\) square units and the height is \(H\) units, then find the value of \(\frac{AH}{V}\).

22. If the volume of a right circular cone is \(X\) cubic units, the area of its base is \(Y\) square units, and its height is \(Z\) units, then what is the value of \(\frac{YZ}{X}\)?

23. If the curved surface area of a right circular cylinder is \(c\) square units, the radius of the base is \(r\) units, and the volume is \(v\) cubic units, then find the value of \(\frac{cr}{v}\).

24. If the curved surface area of a right circular cylinder is \( a \) square units, the radius of its base is \( r \) units, and the volume is \( v \) cubic units, then determine the value of \( \cfrac{ar}{v} \).

25. If a right circular cone has a volume of \(x\) cubic units and a base area of \(y\) square units, then its height is _____.

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. 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

28. If the curved surface area of a right circular cylinder is \(C\) square units, the radius of the base is \(r\) units, and the volume is \(V\) cubic units, then determine the value of \(\cfrac{Cr}{V}\).

29. If the volume of a right circular cone is \(V\) cubic units, the area of the base is \(A\) square units, and the height is \(H\), then what is the value of \(\frac{AH}{V}\)?

30. If the volume of a right circular cone is \(V\) cubic units, the area of its base is \(A\) square units, and its height is \(H\) units, then find the value of \(\frac{AH}{V}\).