Question

14. The 10th grade teachers are creating end-of-year awards for the students who have demonstrated the most growthin their classes. The teachers purchase pyramid-shaped trophies and need to paint all sides of each trophy goldbefore the ceremony. Below, the square base of the trophy and one of the sides are shown. If each gallon of goldpaint can cover 400 square feet, what is the maximum number of trophies they can paint with one gallon?possible answers:(A) 10(B) 17(C) 22.5(D) 38

Answer 1

Given:

• Length of each side of the square base = 2.5 ft

,

• Base of triangle = 2.5 ft

,

• Height of triangle = 3.25 ft

,

• Area each gallon can cover = 400 square feet.

Let's find the number of trophies they can paint with one gallon.

Let's find the surface area of the square pyramid.

To find the surface area, apply the formula:

$SA=A+\frac{1}{2}ps$

Where:

A is the area of the square base = 2.5 x 2.5 = 6.25 square ft.

p is the perimeter of the square base = 2.5 x 4 = 10 feet

s is the slant height = 3.25 ft

Thus, we have:

$\begin{gathered} SA=6.25+\frac{1}{2}*10*3.25 \\ \\ SA=6.25+5*3.25 \\ \\ SA=38.75\text{ square feet} \end{gathered}$

The surface area of each pyramid trophy is 38.75 square feet.

To find the maximum number of trophies they can paint with one gallon(400 square feet), we have:

$\frac{400}{38.75}=10.3$

Therefore, the maximum number of trophies they can paint with one gallon is 10 trophies.

ANSWER:

A. 10