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

The correct answer would be 5 inches.

Explanation:

Answer 2

Answer: 5 inches

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=
`(1)/(3)*\ a^2h`

Therefore, volume of square right pyramid made by all of clay=
`(1)/(3)*\ a^2h`=48 cubic inches

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

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

`\\\Rightarrow\ l=√(3^2+4^2)\\\Rightarrow\ l=√(9+16)\\\rightarrow\ l=√(25)\\\Rightarrow\ l=5`

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