Question

Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. Which is the slant height of the pyramid if Helen uses all the clay? 3 inches 4 inches 5 inches 6 inches

Answer 1

Answer:

The correct answer would be 5 inches.

Step-by-step explanation:

Answer 2

Answer: 5 inches

Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = $a^2=6^2=36\ inches^2$

we know that volume of square right pyramid=$\frac{1}{3}\times\ a^2h$

Therefore, volume of square right pyramid made by all of clay=$\frac{1}{3}\times\ a^2h$=48 cubic inches

$\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}$

Now, slant height $l=\sqrt{(\frac{a}{2})^2+h^2}$

$\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5$

The slant height of the pyramid if Helen uses all the clay=5 inches