Question

The volume of a right rectangular solid is 1536 ft3. Find the height of the solid, if the length is 2 times the width, and the height is twice the perimeter of the base.

Answer 1

Answer:

Height: 48 feet.

Step-by-step explanation:

Let W represent width of the rectangular solid.

We have been given that length is 2 times the width, so the length of the solid would be $2W$.

We know that the perimeter of base of the cuboid is equal to 2 times sum of length and width.

We are also told that the height is twice the perimeter of the base.

$H=2(2L+2W)$

$H=2(2*2W+2W)$

$H=2(4W+2W)=2*6W=12W$

We know that volume of cuboid is equal to length times width time Height.

We have been given that volume of a right rectangular solid is 1536 $\text{ft}^3$. We can represent our given information as:

$L\cdot W\cdot H=1536$

Upon replacing length and height in terms of width, we will get:

$2W\cdot W\cdot 12W=1536$

$24W^3=1536$

$\frac{24W^3}{24}=\frac{1536}{24}$

$W^3=64$

Take cube root of both sides:

$\sqrt[3]{W^3}=\sqrt[3]{64}$

$W=4$

Therefore, the width of the solid is 4 feet.

Let us find Height of the solid as:

$H=12W\Rightarrow12(4)=48$

Therefore, the height of the rectangular solid is 48 feet.