Question

a small box measures 12 in. by 9 in. by 10 in. high. find the volume of the box.
in.³
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question 3
0/1 pt 4 99 details
for a rectangular solid with length 20 ft, width 8 ft, and height 5 ft.
find the a) volume and b) surface area.
volume: ft³ surface area: ft²
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Explanation:

First Problem (Small Box Volume)

Step1: Recall volume formula for rectangular box

The volume \( V \) of a rectangular box (or rectangular prism) is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Substitute the given values

Here, \( l = 12 \) in, \( w = 9 \) in, and \( h = 10 \) in. Substituting these into the formula: \( V = 12 \times 9 \times 10 \)

Step3: Calculate the product

First, calculate \( 12 \times 9 = 108 \), then \( 108 \times 10 = 1080 \)

Step1: Recall volume formula for rectangular solid

The volume \( V \) of a rectangular solid is \( V = l \times w \times h \), where \( l = 20 \) ft, \( w = 8 \) ft, \( h = 5 \) ft.

Step2: Substitute and calculate

Substitute the values: \( V = 20 \times 8 \times 5 \). First, \( 20 \times 8 = 160 \), then \( 160 \times 5 = 800 \)

Step1: Recall surface area formula for rectangular solid

The surface area \( SA \) of a rectangular solid is given by \( SA = 2(lw + lh + wh) \), where \( l = 20 \) ft, \( w = 8 \) ft, \( h = 5 \) ft.

Step2: Calculate each term inside the parentheses

• Calculate \( lw = 20 \times 8 = 160 \)
• Calculate \( lh = 20 \times 5 = 100 \)
• Calculate \( wh = 8 \times 5 = 40 \)

Step3: Sum the terms and multiply by 2

First, sum the terms: \( 160 + 100 + 40 = 300 \). Then multiply by 2: \( SA = 2 \times 300 = 600 \)

Answer:

\( 1080 \)

Second Problem (Rectangular Solid)

a) Volume