7.GR.A.2: Describe the two-dimensional figures that result from slicing three-dimensional figures (e.g., right rectangular prisms, right cylinders) with a plane. Use the resulting shapes to explain how the structure of the solid connects to volume and surface area.

Describe the two-dimensional figures that result from slicing three-dimensional figures (e.g., right rectangular prisms, right cylinders) with a plane. Use the resulting shapes to explain how the structure of the solid connects to volume and surface area.

Example Problems

Mariko has an

80 : 1

scale-drawing of the floor plan of her house. On the floor plan, the dimensions of her rectangular living room are

1 \frac{7}{8}

inches by

2 \frac{1}{2}

inches.

What is the area of her real living room in square feet?

Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter which he finds, to the

\text{nearest millimeter}

, to be

5 \text{ centimeters}

.

a. How large is the possible error in Juan's measurement of the diameter of the circle? Explain.

b. As a percentage of the diameter, how large is the possible error in Juan's measurement?

c. To find the area of the circle, Juan uses the formula

A = \pi r^2

where

A

is the area of the circle and

r

is its radius. He uses

3.14

for

\pi

. What value does Juan get for the area of the circle?

d. As a percentage, how large is the possible error in Juan's measurement for the area of the circle?

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least

15 \text{ inches}

deep. The sand under both swing sets was only

12 \text{ inches}

deep when they started.

The rectangular area under the small swing set measures

9 \text{ feet} \times 12 \text{ feet}

and required

40 \text{ bags}

of sand to increase the depth by

3 \text{ inches}

. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is

1.5 \text{ times}

as long and

1.5 \text{ times}

as wide as the area under the small swing set?

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