Question

What is the slant height of a square pyramid of base perimeter 80 centimeters and volume 1600 cubic centimeters?

• A. 244
• B. $61\sqrt{2}$
• C. 61
• D. 122

Answer 1

The correct option is B

$61\sqrt{2}$

Given that base perimeter of the square pyramid = $80cm$
$\therefore baseedge=\frac{Baseperimeter}{4}=\frac{80}{4}=20$

$⟹Basearea=400c{m}^2$
Now, Volume of a square pyramid = $\frac{1}{3}\times Basearea\times Height=1600c{m}^3$
i.e., $\frac{1}{3}\times 400\times Height=1600$
$⟹Height=\frac{1600\times 3}{400}=12cm$
Thus, Slant height = $\sqrt{(Height{)}^2+(Halfthebaseedge{)}^2}=\sqrt{(12{)}^2+(10{)}^2}=\sqrt{244}=61\sqrt{2}$