Geometry Answers

4. The lateral edge of a square prism is 20 cm long and it is inclined at an angle of 60 degrees with the base. If the volume of the prism is 1,200 cm3, determine the base edge.

5. The total area of a regular tetrahedron is 110.85 m2, determine its base edge.

6. If the lateral area of a right circular cylinder is 90 cm2 and its volume is 225 cm3, find its radius.

1. A frustum of a regular hexagonal pyramid has an upper base edge of 5m and a lower base edge of 8.5m. Its lateral area is 160m2. Determine the slant height of the frustum.

2. A regular square pyramid has an altitude of 12 m and volume of 196 m3. Determine the slant height of the pyramid.

3. A regular square pyramid has a height of 8m. If the slant height makes an angle of 45º with the base, find the lateral
area of the pyramid

1. A frustum of a regular hexagonal pyramid has an upper base edge of 5m and a lower base edge of 8.5m. Its lateral area is 160m2. Determine the slant height of the frustum.

2. A regular square pyramid has an altitude of 12 m and volume of 196 m3. Determine the slant height of the pyramid.

3. A regular square pyramid has a height of 8m. If the slant height makes an angle of 45º with the base, find the lateral area of the pyramid.

4. The lateral edge of a square prism is 20 cm long and it is inclined at an angle of 60 degrees with the base. If the volume of the prism is 1,200 cm3, determine the base edge.

25. Find the midsection of a frustum of a square pyramid if its lower base is 20 cm on a side, its upper base is 12 cm on a side, and the altitude of the frustum is 14 cm.

24. A prismatoid has an upper base of 90%, a lower base of 2100%, an altitude of 100 cm, and a midsection of 120? What is its volume?

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2

21. What is the radius of the sphere?
22. What is the altitude of the tetrahedron?.
23. If a sphere is inscribed in a cube of side What is the volume of the sphere?

The base of a right prism is an equilateral triangle whose edges is 10cm each and its lateral edge is 80cm.

19. Find its volume in cm3.
20. Determine the total area of the prism in cm2

__17. A rectangular solid whose dimensions are 4cm, 8cm, and 12cm is inscribed in a sphere. What is the diagonal of the rectangular solid?

_18. In question 17, what is the surface area of the sphere in ¹?

16. Identify a polyhedron with two congruent bases that lie in parallel planes, and whose every section that is parallel to a base has the same area as that of the base.

15. What is the solid generated by rotating a right triangle about one of its legs as an axis?