HW: Volume Review KEY
Name: ____________________________________________
Date Assigned: April 28 Sec: ________
1) Draw and label each solid. Use dashed lines to show the hidden edges.
a. A triangular pyramid whose base is an equilateral triangular region (use the proper marks to show
that the base is equilateral).
b. A hexahedron with two trapezoidal faces
2) Fill in the blank.
a. A lateral face of a pyramid is always a ___triangular_ region.
b. Every slice of a prism cut parallel to the bases is __congruent__ to the base.
c. When the lateral surface of a right circular cone is unwrapped and laid flat, it is a ___sector of a
circle_________.
d. When the lateral surface of a right cylinder is unwrapped and laid flat, it is a rectangle.
e. All slices of a sphere passing through the sphere’s center are _congruent/great circles____.
f.
A regular triangular pyramid is also called a __tetrahedron__.
g. A regular hexahedron is also called a _____cube_____.
h. A solid with seven faces is called a ____heptahedron__________________________________.
i.
A face that is not a base is called ____a lateral face_____.
j.
All _lateral_ (answer from j.) faces of an oblique prism are __parallelograms_____.
k. The axis of a right cylinder or prism is __perpendicular_____ to the base.
3) __403 barrels__ As bad as tanker oil spills are, they are only about 12% of the 3.5 million tons of oil that
enters the ocean each year. The rest comes from routine tanker operations, sewage treatment plants’
runoff, natural sources, and offshore oil rigs. One months’ maintenance and routine operation of a single
supertanker produces up to 17,000 gallons of oil sludge that gets into the ocean! If a cylindrical barrel is
about 1.6 feet in diameter and 2.8 feet tall, how many barrels are needed to hold 17,000 gallons of oil
sludge? Recall that a cubic foot of water is about 7.5 gallons.
4) __3 cm.___ A hemisphere has a volume of 𝟏𝟖𝝅 𝒄𝒎.𝟑 . Find its radius.
5) __𝟐𝟒𝟎√𝟑 𝒄𝒎.𝟑 ≈ 𝟒𝟏𝟓. 𝟔𝟗 𝒄𝒎.𝟑 __ Find the volume. All measurements are in centimeters. Give the exact
answer, and then round the answer to the nearest hundredth.
6) _𝑽 = 𝟒𝝅𝒙𝒚𝟐 __ Use algebra to express the volume of the following solid.
7) _𝟔√𝟏𝟕 𝒄𝒎.__ The volume of a pyramid with an isosceles triangular base is 240 square centimeters and its
height is 20 cm. The base of the base triangle is 6 cm. What is the length of the other two sides of the base?
8) __≈45.7 cubic centimeters A square pyramid resting on its base is filled to half its height with 320 cubic
centimeters of water. How much water is needed to finish filling the pyramid? Round your answer to the
nearest tenth of a cubic centimeter.
9) __679 cubic centimeters__ What is the volume of the slice removed from this right cylinder? Give your
answer to the nearest cubic centimeter.
10) * ___________________ Dennis’s scoop of ice cream has a radius of 2cm. It rests in a cone that has a radius
of √𝟑 cm. at the widest part, and the scoop is tangent to each line containing a slant height of the cone. He
eats some of the ice cream and then finds that the remainder of the ice cream can be pushed down to fill the
cone exactly. How many cubic centimeters of ice cream did he eat?