7th Grade Math

572 Volume and Surface Area

You can also use the formula for the volume of a pyramid to find a

missing height.

Find the Height of a Pyramid

A triangular pyramid has a volume of 44 cubic meters. It has an

8-meter base and a 3-meter height. Find the height of the pyramid.

V = _^13 Bh Volume of a pyramid h

3 m 8 m

44 = 31 ( 21 · 8 · (^3) ) h V = 44, B = 21 · 8 · 3
44 = 4 h Multiply.
^444 = ^44 h Divide by 4.
11 = h Simplify.
The height of the pyramid is 11 meters.
b. A triangular pyramid has a volume of 840 cubic inches. It has a
base of 20 inches and a height of 21 inches. Find the height of
the pyramid.
SAND SCULPTURES A model of a sand
12 in.
12 in.
12 in.
sculpture is shown at the right. Find the
volume of the square pyramid.
V = 31 Bh Volume of a pyramid
V = ^13 (12 · 12) 12 B = 12 · 12, h = 12
V = 576 Simplify.
The volume is 576 cubic inches.
c. MODELS Kamilah is making a model of the Food Guide Pyramid
for a class project. The model is a square pyramid with a base
edge of 4 inches and a height of 5 inches. Find the volume of
plaster needed to make the model. Round to the nearest tenth.
d. STADIUMS The Pyramid Arena
in Memphis, Tennessee, is a
square pyramid 321 feet tall.
The base has 600-foot sides.
Find the volume of the
pyramid.
Multiplying Fractions
To fi nd ^13 · 21 · 8 · 3,
multiply 31 · 21 and 8 · 3
to get ^16 and 24, then
fi nd _^16 of 24.
Real-World Link
The U.S. Department
of Agriculture
recommends that
teenagers eat at least
three ounces of whole
grains, plenty of dark
green and orange
vegetables, a variety
of fruit, calcium-rich
foods, lean meats,
and a limited intake
of oils each day.
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