QuestionI. Word Problems. Solve the following problems and show your solutions.
1. A cone has a radius of 4 cm and a height of 9 cm . Find the volume of the cone.
2. A cone has a slant height of 10 cm and a base radius of 6 cm . Calculate the surface area of the cone.
3. The volume of a cone is $150 \mathrm{~cm}^{3}$ and its base radius is 5 cm . Determine the height of the cone.
4. A cone has a total surface area of $150 \mathrm{~cm}^{2}$ and a slant height of 12 cm . Find the radius of the base.
5. A cone has a volume of $200 \mathrm{~cm}^{3}$ and a base radius of 5 cm . Find the slant height of the cone.
6. A square pyramid has a base edge of 8 cm and a height of 15 cm . Calculate the volume.
7. A triangular pyramid has a base area of $20 \mathrm{~cm}^{2}$ and a slant height of 10 cm . If each triangular face has an area of $25 \mathrm{~cm}^{2}$, find the total surface area.
8. The volume of a rectangular pyramid is $240 \mathrm{~cm}^{3}$ and the base dimensions are 6 cm by 4 cm . Find the height of the pyramid.
9. A pyramid has a volume of $500 \mathrm{~cm}^{3}$ and a height of 10 cm . If the base is a regular hexagon, find the area of the base.
10. A pyramid has a base side of 9 cm and a total surface area of $648 \mathrm{~cm}^{2}$. Calculate the slant height if the height of the pyramid is 12 cm .
11. A frustum of a cone has a lower base radius of 7 cm , an upper base radius of 4 cm , and a height of 10 cm . Find the volume.
12. Find the surface area of a frustum with a lower base radius of 6 cm , an upper base radius of 3 cm , and a slant height of 8 cm .
13. A frustum of a cone has a volume of $400 \mathrm{~cm}^{3}$, a height of 12 cm , and radii of 5 cm and 3 cm for the lower and upper bases. Find the slant height.
14. The frustum of a cone has a total surface area of $300 \mathrm{~cm}^{2}$, lower base radius of 5 cm , and an upper base radius of 3 cm . Find the height of the frustum if the slant height is 7 cm .
15. A frustum with a height of 8 cm has a volume of $320 \mathrm{~cm}^{3}$. The radius of the lower base is 6 cm and the radius of the upper base is unknown. Find the radius of the upper base.