A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox? (A) 20 (B) 40 (C) 60 (D) 80 (E) 100

(D) 80 ft³

Step-by-step explanation:

The volume volume of the sandbox is = L * W * H

Where L = Length, W = width, H = Height.

A sandbox has the same shape as a cuboid.

A cuboid is a solid shape with rectangular base and sides. It has six rectangular faces if all sides are closed.

From the question,

LWH = 10ft³ ... (1).

If a similar sandbox twice as long, twice as wide and twice as high.

∴ L₍n₎ = 2L, W₍n) = 2W, H₍n₎ = 2H

Where L₍n₎, W₍n), H₍n₎ is the new Length, new Width and new Height of the similar sandbox.

∴L₍n₎ * W₍n) * H₍n₎ = 2L * 2W * 2H

and Volume of the new sandbox = L₍n₎ * W₍n) * H₍n₎

⇒Volume of the new sandbox = 2 * 2 * 2 * L*W*H

Volume of the new sandbox = 8 * LWH ... (2)

In equation (1) LWH = 10ft³.

Substituting the value in equation (2)

∴Volume of the new (similar) sandbox = 8 * 10

=80ft³.

Therefore the capacity of the second sandbox in cubic feet is 80.

The answer is option (D).