MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of solids.

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Geometry Mini-Lesson
Jacob has two rectangular sheets of metal that
measure 10 centimeters (cm) by 20 cm. He formed
Box A by cutting a 3 cm square from each corner
of the metal sheet and folding up the flaps to
form a rectangular prism with an open top.Jacob
then formed Box B by cutting a 1 cm square from
each corner of the other sheet of metal and
folding up the flaps to form another rectangular
prism with an open top.What is the difference
in the volumes, in cubic centimeters, of Box A
and Box B?

1. 20 cubic cm
2. 24 cubic cm
3. 32 cubic cm
4. 48 cubic cm

MA.912.G.7.5 Explain and use formulas for
lateral area, surface area, and volume of solids.
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Geometry Mini-Lesson
Mr. Tran built a rectangular sandbox for the
local park as shown below. He wants to fill it
with sand that comes in 50-pound bags. If each
bag contains about 0.75 cubic feet of sand, how
many bags are needed to fill the sandbox?

1. 120
2. 140
3. 160
4. 190

MA.912.G.7.5 Explain and use formulas for
lateral area, surface area, and volume of solids.
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Geometry Mini-Lesson
Samir built a wooden storage shed in the shape of
a cube with sides 10 feet on each side capped by
a right square pyramid, as shown by the figure
below. The height of the entire figure is 22
feet. Samir needs to paint all of the lateral
surfaces of the shed, including the roof but not
including the floor. What is the surface area
that will need to be painted?

1. 640 sq feet
2. 660 sq feet
3. 760 sq feet
4. 1400 sq feet

MA.912.G.7.5 Explain and use formulas for
lateral area, surface area, and volume of solids.
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Geometry Mini-Lesson
MA.912.G.7.5 Explain and use formulas for
lateral area, surface area, and volume of solids.
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Geometry Mini-Lesson
A glass right cylinder with diameter 12
centimeters (cm) is partially filled with water
to a level of 16 cm as shown in the figure
below.If a solid metal cube with an edge length
of 7 cm is dropped into the cylinder, which of
the following is closest to the height of the new
water level?

1. 13 cm
2. 17 cm
3. 18 cm
4. 19 cm

MA.912.G.7.5 Explain and use formulas for
lateral area, surface area, and volume of solids.