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Compilation of Problems in Solid Mensuration

1. The sum of the interior angles of a polygon is 540°. Find the number of sides.

2. A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon.

3. The volume of a sphere is 36π cu. m. What is its surface area?

4. One side of a regular octagon is 2. Find the area of the region inside the octagon.

5. The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12 and 14 units. What is the area of the largest circle?

6. If the sides of a parallelogram and an included angle are 6, 10 and 100° respectively, find the length of the shorter diagonal.

7. A trapezoid has an area of 36 m^2 and an altitude of 2 m. Its two bases have ratio of 4:5. What are the lengths of the bases?

8. The sides of a right triangle are 8, 15 and 17 units. If each side is doubled, how many square units will the area of the new triangle?

9. Find the measure of each interior angle in degrees of a regular dodecagon.

10. If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle.

11. A metal washer 1-inch in diameter is pierced by 1/2 inch hole. What is the volume of the washer if it is 1/8 inch thick?

12. What polygon has 27 diagonals?

13. The volume of the two spheres is in the ratio 27:343 and the sum of their radii is 10. Find the radius of the smaller sphere.

14. A regular hexagonal pyramid has a slant height of 4 cm and the length of each side of the base is 6 cm. Find the lateral area.

15. What is the area of an isosceles right triangle if its perimeter is 6.6824?

16. What is the distance in cm between two vertices of a cube which are farthest from each other, if an edge measures 8 cm?

17. The area of the rhombus is 132 sq. m. If its shorter diagonal is 12 m, find the longer diagonal.

18. One of the diagonals of a rhombus is 25 units and its area is 75 u^2. Determine the length of the sides.

19. Find the area of a parabola having a span of 30 m and a height of 20 m.

20. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon.

21. The lateral area of the right circular water tank is 92 cm^2 and its volume is 342 m^3. Determine its radius.

22. A cone and a cylinder have the same height and the same volume. Find the ratio of the radius of the cone to the radius of the cylinder.

23. It is desired that the volume of the sphere be tripled. By how many times will the radius be increased?

24. What is the area of a parabola with a base of 15 cm and a height of 20 cm? The circumference of a great circle of a sphere is 18π. Find the volume of the sphere

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