Question

q12. determine the surface area of a rectangular solid that has a height of 10 mm, a width of 17 mm, and a length of 12 mm. what is the volume of this solid?

Explanation:

Step1: Recall surface area formula for rectangular solid

The formula for the surface area \( S \) of a rectangular solid (also called a rectangular prism) with length \( l \), width \( w \), and height \( h \) is \( S = 2(lw + lh + wh) \).
Given \( l = 12 \) mm, \( w = 17 \) mm, \( h = 10 \) mm.
First, calculate each product:

• \( lw = 12\times17 = 204 \)
• \( lh = 12\times10 = 120 \)
• \( wh = 17\times10 = 170 \)

Step2: Calculate surface area

Now, substitute these into the surface area formula:
\( S = 2(204 + 120 + 170) \)
First, add the terms inside the parentheses: \( 204+120 + 170=494 \)
Then, multiply by 2: \( S = 2\times494 = 988 \) square millimeters.

Step3: Recall volume formula for rectangular solid

The formula for the volume \( V \) of a rectangular solid is \( V=l\times w\times h \).

Step4: Calculate volume

Substitute \( l = 12 \), \( w = 17 \), \( h = 10 \) into the formula:
\( V = 12\times17\times10 \)
First, calculate \( 12\times17 = 204 \), then \( 204\times10 = 2040 \) cubic millimeters.

Answer:

Surface Area: \( 988 \) \( \text{mm}^2 \)
Volume: \( 2040 \) \( \text{mm}^3 \)