Question

practice– volume and surface area of 3d figures
date
block
volume\tfigure\tsurface area
21×7=
23
198 ft²
0=

1. calculate the volume and surface area of a rectangular prism with length 21 ft, width 9 ft, height 7 ft
2. calculate the volume and surface area of a rectangular prism with length 11 cm, width 8 cm, height 20 cm
3. calculate the volume and surface area of a rectangular prism (cereal box) with length 8 in, width 2 in, height 12 in

Explanation:

For a rectangular prism, the formulas are:
Volume $V = l \times w \times h$
Surface Area $SA = 2(lw + lh + wh)$

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Figure 1 (9 ft, 21 ft, 7 ft)

Step1: Calculate Volume

$V = 9 \times 21 \times 7 = 1323 \text{ ft}^3$

Step2: Calculate Surface Area

$SA = 2(9 \times 21 + 9 \times 7 + 21 \times 7) = 2(189 + 63 + 147) = 2(399) = 798 \text{ ft}^2$

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Figure 2 (11 cm, 8 cm, 20 cm)

Step1: Calculate Volume

$V = 11 \times 8 \times 20 = 1760 \text{ cm}^3$

Step2: Calculate Surface Area

$SA = 2(11 \times 8 + 11 \times 20 + 8 \times 20) = 2(88 + 220 + 160) = 2(468) = 936 \text{ cm}^2$

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Figure 3 (8 in, 2 in, 12 in)

Step1: Calculate Volume

$V = 8 \times 2 \times 12 = 192 \text{ in}^3$

Step2: Calculate Surface Area

$SA = 2(8 \times 2 + 8 \times 12 + 2 \times 12) = 2(16 + 96 + 24) = 2(136) = 272 \text{ in}^2$

Answer:

1. Volume: $1323 \text{ ft}^3$, Surface Area: $798 \text{ ft}^2$
2. Volume: $1760 \text{ cm}^3$, Surface Area: $936 \text{ cm}^2$
3. Volume: $192 \text{ in}^3$, Surface Area: $272 \text{ in}^2$