Volume Applications
1.
a)
Ice cream is sold in stores in cylindrical containers. The containers are 21 cm
high with a radius of 10 cm. Determine how much ice cream is in each container.
b)
Each scoop of ice cream is a sphere of diameter 4.2 cm. Determine how much
ice cream is in each scoop.
c)
How many scoops are in each container?
d)
If one scoop sells for 86¢, how much money will the ice cream store make for
each full container of ice cream that it sells in cones?
2.
Storm sewers are hollow cylinders with outside radius of 0.9 m and inside radius
0.7 m. If a section of storm sewer is 2.5 m long, what volume of concrete is
needed to make it?
b) What volume of water can flow through it?
3.
Math-O’s cereal is sold in a single-serving size box in the shape of a rectangular
prism of dimensions 5 cm by 4 cm by 10cm.
a) Calculate how much cereal this box can hold.
b) If the dimensions of the box are doubled, what do you think will happen to the
volume?
c) Test your hypothesis by calculating the volume of the box with the new
dimensions.
4.
a) Calculate the capacity of the can of soup pictured below.
6 cm
10 cm
b) What volume of soup would the can hold if it was changed to a cone with the
same base and height?
c) If the original can of soup sells for $1.38, what should the conical shape soup
can sell for?
Volume Applications
5) The surface area of a cube with side length 6cm, a cylinder with a radius of
2.71cm and a height of 10cm, and a cone with radius of 5.21 cm and a slant
height of 8 cm would be approximately 216 square cm. If a manufacturer were to
choose one of these packaging options, each would cost the same amount to
build. Which packaging would allow the company to ship the most product?
6) Volume is great for measuring liquid. You can figure out how much water a
pool holds by getting its length, width, and depth. The general rule is 1 cubic foot
= 7.48 gallons. Assume your neighbors have a big, perfectly round pool with a
diameter of 30 feet and a depth of 5 feet. How much water would that pool hold?
7) You have a can of soda and want to find out how tall it is by using its radius
and its volume. Assume you pour the soda into a measuring glass and find that
the can holds 12.1 ounces of soda. If .55 ounces = 1 cubic inch, what is the
volume of liquid in your can (how many cubic inches)?
b) Your can has a diameter of 2 inches. Use the volume and diameter to find out
how tall the can is.
8) Wet snow weight .575 times its volume in cubic inches divided by 144. Find
the volume of snow someone would shovel off a driveway measuring 25 ft long
and 10 ft wide after it snows 8 inches. (Hint: convert to inches before finding
volume)
b) Calculate the weight of the snow removed from the driveway.
9) A grain silo is comprised of a cylindrical base with a hemispherical top. If the
radius of the silo is 7m and the total height is 50 meters, find the volume of grain
that could be stored in the silo.
b) If the farmer uses 450 cubic meters per day, in how many days would the silo
be emptied?
10) A m o vin g co m pa n y is t ryin g t o st ore b o xe s in a st o rage ro o m
wit h a le n gt h of 5 m , wid t h of 3 m a nd h e igh t of 2 m. Ho w m a n y
b o xe s ca n f it in th is sp a ce if ea ch is 1 0 cm lo n g, 6 cm wid e a n d 4
cm h igh ?