Answer:
(D)80 ft³
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).