Question

what is the surface area of the prism?
a 156 sq in.
b 936 sq in.
c 1,872 sq in.
d 5,184 sq in.
image of a rectangular prism with dimensions 24 in., 12 in., 18 in.
question 3
sarah is filling a glass sphere with decorative sand. the radius of the sphere is 2 inches. which is closest to the minimum amount of sand sarah needs to completely fill the glass sphere?
a partially visible
b partially visible
c partially visible

Explanation:

Step1: Recall the formula for the surface area of a rectangular prism.

The formula for the surface area \( SA \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( SA = 2(lw + lh + wh) \).

Step2: Identify the values of \( l \), \( w \), and \( h \).

From the diagram, \( l = 24 \) in, \( w = 12 \) in, and \( h = 18 \) in.

Step3: Substitute the values into the formula.

First, calculate each product:

• \( lw = 24 \times 12 = 288 \)
• \( lh = 24 \times 18 = 432 \)
• \( wh = 12 \times 18 = 216 \)

Then, sum these products: \( 288 + 432 + 216 = 936 \)

Finally, multiply by 2: \( SA = 2 \times 936 = 1872 \) square inches.

Answer:

C. 1,872 sq in.