Question

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

Answer 1

The slant height of the pyramid will be 5 inches.

Given Information and Formula Used

Volume of the clay = 48 cubic inches

Edge of the square base of the pyramid, a= 6 inches

Volume of the pyramid = (1/3) × Base Area × Height

Pythagoras Theorem, l² = x² + h²

Here, l is the hypotenuse, x is the base and $h$ is the height in a right angle triangle.

Calculating the Height, h of the Pyramid

Volume of the pyramid = Volume of the clay

Volume of the pyramid, V= 48 cubic inches

Base Area of the pyramid, B = a²

⇒ B = 6² square inches

⇒ B = 36 square inches

∵ V = (1/3)×B×H

$\frac{1}{3}*36*h = 48$

∴ $h = \frac{48*3}{36}$

⇒ h = 4 inches

Calculating the Slant Height, l of the Pyramid

Applying Pythagoras Theorem to determine the slant height,

l² = x² + h²

Here, we have x=a/2

$l^{2} = \frac{a^{2} }{4} + b^{2}$      

$l^{2} = \frac{6^{2} }{4} + 4^{2}$

$l = \sqrt{9+16}$

$l=\sqrt{25}$

l =5 inches

Thus, the slant height of the solid right pyramid with a square base made by Helen is 5 inches.

Learn more about a pyramid here:

https://brainly.com/question/17615619

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