Volume word problems with cones, cylinders and spheres
1. A soap company changes the design of its soap from a cone to a sphere. The cone had a
height of 3inches and a radius of 2 inches. The sphere has a diameter of 3 inches. How
much more soap, in cubic inches, does the new design contain than the old design?
2. A yellow sphere of radius 5 is cut by red, blue, and green planes passing through its
center. This partitions the solid into eight equal parts, three of which are pictured below.
3. What is the volume of each part?
4. What is the volume of the solid?
5. Water is poured into a rectangular container 20 cm long, 14 cm wide, and 9 cm high,
until it is 5/6 full. All this water is then poured into an empty cylindrical container with
a radius of 15 cm and height 20 cm. What is the height of the water in the cylinder
to the nearest whole centimeter?
6. A conical glass holds 131 cubic centimeters of water. It has a height of 5 centimeters.
To the nearest centimeter, what is the radius of the top of the glass?
7. A grain silo is shaped like a cylinder with a hemispherical top. The height of the
cylindrical portion is 20meters, with a radius of 9 meters. The silo is full of grain.
What fraction of the grain is in the cylindrical portion of the silo?
8. Consider the following hemisphere, cone, and cylinder:
Call the volume of these three solids V1,V2, and V3, in that order. Which of the
following are true?
a)
V1+V2<V3
b)
V1+V2=V3
c)
V1+V2>V3
d)
Not enough information to determine
9. The moon has a radius of 1736 kilometers. The earth has a radius of 6371 kilometers.
How many times as large is the volume of the Earth as the volume of the moon,
rounded to the nearest whole number?
10. Marion forms a ball of clay with a radius of 2 in. He then reforms the clay into a
cylinder of radius 3 in. What is the height of the cylinder?
11. Yohan is blowing up a spherical balloon. He knows that he is able to blow 108π cubic
centimeters of air with every breath. It takes him 9 breaths to fully inflate the balloon.
What is the radius of the balloon when it is fully inflated?
12. A washing machine is being redesigned to handle a greater volume of water. One part is
a pipe with a radius of 3 inches and a length of 11 inches. It gets replaced with a pipe
of radius 4 inches, and the same length. How many more cubic inches of water can
the new pipe hold?