ACTIVITY # 5
Solve the following problems. Show clean and complete solutions for each
number.
1. The volume of a dodecahedron is 3,921.92 m 3. What is the surface area of the
dodecahedron?
A. 1,321.60 m 2
C. 1,627.80 m 2
B. 1,214.50 m 2
D. 1,112.70 m 2
2. Each face of a regular octahedron has an area of 12 cm 2. Find the surface area of the
octahedron.
A. 72 cm2 C. 84 cm2
B. 68 cm2 D. 96 cm2
3. A right prism has a base in the form of a hexagon inscribed in a circle with radius 8
cm. The height of the prism is 12 cm. Compute its total surface area.
A. 909 cm2 C. 1,997 cm2
B. 792 cm2 D. 1,896 cm2
4. A trough whose ends are isosceles trapezoids with vertical axis is 5 m long. The
lower base of the trapezoid is 1 m and the upper base is 3 m. The non – parallel sides
of the trapezoid measure 2 m. Compute the capacity( volume ) of the trough.
A. 13.60 m3 C. 16.27 m3
3
B. 17.32 m D. 11.12 m3
5. A truncated prism has a base in the form of a right triangle with perpendicular sides 10
cm and 16 cm. The lateral edges perpendicular to the base are 12 cm, 16 cm, and 14
cm, respectively. Compute the volume of the truncated prism.
A. 1,120 cm3 C. 880 cm3
3
B. 940 cm D. 1,210 cm3
6. The lateral edge of the frustum of a regular pyramid is 2.4 m long. The upper base is
a square with sides 1.2 m by 1.2 m, and the lower base is a square with sides 3 m by
3 m. Compute the volume of the frustum.
A. 7.12 m3 C. 8.36 m3
B. 6.94 m3 D. 9.52 m3
7. A spherical wedge has a radius of 6 cm and a volume of 60.32 cm 3. Compute the
surface area of its lune.
A. 28.42 cm2 C. 32.14 cm2
B. 30.16 cm2 D. 24.86 cm2
8. A tank is in the form of a frustum of a sphere with radius 4m, the bases are cut by
parallel planes on opposite sides from the center of the sphere and at distances 1 m
and 2 m respectively. Find the capacity of the tank in liters.
A. 123,942 lit C. 141,372 lit
B. 126,972 lit D. 161,872 lit
9. A solid sphere has a diameter of 6 m. A plane cuts the sphere into two segments with
the smaller segment has a height of 2 m. Compute the ratio of the area of the zone of
the smaller segment to that of the area of the zone of the bigger segment.
A. 1:2 C. 1:4
B. 1:3 D. 1:6
10. A hemispherical container with a radius of 10 cm is filled with water to a depth of 6 cm.
Find the volume of water in the tank.
A. 870.26 cm3 C. 904.78 cm3
B. 720.72 cm3 D. 628.45 cm3
11. A sphere has a radius of 12. Compute the volume of the largest cube that can be
inscribed in the sphere.
A. 2,168.34 C. 2,564.78
B. 2,268.12 D. 2,660.43
12. The volumes of 2 spheres are in the ratio 27:343 and the sum of their surface areas is
18,221.23739 cm2. Compute the radius of the smaller sphere.
A. 12 cm C. 15 cm
B. 13 cm D. 18 cm
13. A hole with diameter 4 cm is drilled through the axis of a right circular cone with height
10 cm and base diameter 12 cm. Find the remaining volume of the cone after drilling?
A. 279.25 cm3 C. 256.42 cm3
B. 168.38 cm3 D. 187.38 cm3
14. A cone with base area of 50 cm 2 and a height of 10 cm is cut by a plane parallel to
and 4 cm from the base. Find the volume of the smaller cone cut.
A. 18 cm3 C. 24 cm3
B. 36 cm3 D. 40 cm3
15. A lampshade is in the form of a frustum of a cone. The vertical height is 22 cm and the
base diameters are 18 cm and 10 cm respectively. Find the area of the material
needed to make the lampshade.
A. 826.52 cm2 C. 983.44 cm2
2
B. 818.78 cm D. 979.36 cm2
16. A frustum of cone has a volume of 189 m3, and base radii 3 m and 6 m. Find the
perpendicular distance between the bases.
A. 12 cm C. 9 cm
B. 13 cm D. 18 cm
17. A closed cylindrical tank is to be constructed so that its height is to be twice to the
base radius. If the volume of the tank is to be 98 m3, find the area of the material
needed to construct the tank.
A. 126.5 m2 C. 183.4 m2
B. 117.8 m2 D. 179.3 m2
18. One of the great pyramid of Egypt has a rectangular base 100 m x 140 m and the
lateral edge is 240 m. Compute the volume of the pyramid.
A. 1,236,192 m3 C. 1,045,067 m3
3
B. 1,417,228 m D. 1,126,701 m3
19. The base of a solid is a circle of radius 5ft. Find the volume if every section
perpendicular to a fixed diameter of the base is an equilateral triangle with one side on
the base.
A. 722.72 C. 666.67
B. 458.23 D. 288.67
20. A sphere of radius 5 cm and a right circular cone of base radius 5 cm and a right
circular cone of height 10 cm stand on a horizontal floor. Find the vertical distance
from the horizontal floor will a plane cut the 2 solids in equal circular section
A. 2 cm C. 1.5 cm
B. 3 cm D. 2.5 cm
