Assignment 6
1. The Earth’s diameter is approximately four times the moon’s and both bodies are
spheres. What is the ration of their volumes?
2. If 50 steel marbles that are 1 cm in diameter are melted down, will enough steel
result to build a marble that is 4 cm in diameter? Explain.
3. A cone shaped water cup has a height of 8 cm and a radius of 4 cm. If the cup is
filled with water to half its height, what portion of the volume of the cup is filled
with water?
4. Which is a better buy: a grapefruit 5 cm in radius that costs 22 cents or a
grapefruit 6 cm in radius that costs 31 cents? Explain.
5. Suppose a scoop of ice cream that is a sphere with a radius of 5 cm fits exactly
along one of its great circles in a sugar cone, as shown in the figure. Suppose the
ice cream melts and the cone does not absorb any of it. If the cone is 10 cm tall,
will it hold the melted ice cream? If not, how tall would the cone have to be to
hold the melted ice cream?
6. Half of the air is let out of a spherical balloon. If the balloon remains in the shape
of a sphere, how does the radius of the smaller balloon compare with the radius of
the original balloon?
7. A box is packed with 6 soda cans, as in the following figure. What percentage of
the volume of the interior of the box do the cans not occupy?
8. Which will increase the volume of a circular cylinder more: doubling its height or
doubling its radius? Explain.
9. The following sphere, right circular cylinder, and right circular cone have the
same volume. Find the height of the cylinder and the slant height of the cone.
10. A right circular cylinder and a right circular cone share a circular base and have
the same volume. What is the height of the cone?
11. Consider a sphere inside a right circular cylinder just large enough to contain the
sphere.
(a) What fraction of the volume of the cylinder is occupied by the sphere?
(b) What fraction of the surface area of the cylinder is the surface area of the
sphere?
12. Find the volume of the following stand that is cut from a right circular cone.
13. In the following figure, a right circular cylinder is inscribed in a right circular
cone. The height of the cone is 40 cm, the height of the cylinder is 30 cm, and the
radius of the base of the cone is 25 cm. What percent of the volume of the cone
does the cylinder occupy?