Question

The area of each of the four triangular faces of a square shaped pyramid mold as shown is 609 sq. in.

If the height of the mold is 20 in, find the volume of caramel that can be filled in 5 such molds.

• A. 11760 cu.in
• B. 35,280 cu.in
• C. 47,040 cu.in
• D. 58,800 cu.in

Answer 1

The correct option is D 58,800 cu.in

Let the length of the side of square in the pyramid be 'b',
Given, height of triangular face is 29 in.
Area of each triangular face is 609 sq.in.
$\text{Area of each traingular face =}\frac{1}{2}\times base\times height$

$\Rightarrow 609=\frac{1}{2}\times b\times 29$
$\Rightarrow b=42\text{in}$

$\text{Area of base of square pyramid = side x side}=42\times 42$
$=1764\text{sq. in}$

$\text{Volume of pyramid mold =}\frac{1}{3}\times \text{area of base}\times \text{height of pyramid}$
$=\frac{1}{3}\times 1764\times 20$
$=11760\text{cu.in}$
$\therefore$ Volume of caramel that can be filled in 5 such molds $=11760\times 5=58800\text{cu.in}$