A cubical container of surface area 486 sq. ft filled with water

| A cubical container of surface area 486 sq. ft filled with water is emptied into another cylindrical container thus occupying 36% of its volume. What is the volume of cylindrical container?

A. 1826 cubic ft

B. 3125 cubic ft

C. 1624 cubic ft

D. 2025 cubic ft

Please scroll down to see the correct answer and solution guide.

Right Answer is: D

SOLUTION

Let ‘a’ be the edge of cube.

We know that,

Surface area of cube of side ‘a’ = 6a²

⇒ Surface area of the cube = 486 sq. ft

⇒ 6a² = 486

⇒ a² = 486/6 = 81 = 9²

⇒ a = 9 ft

We know that,

Volume of a cube of side ‘a’ = a³

⇒ Volume of the cube = a³ = 9³ = 729 cubic ft.

Volume of cube = 36% of volume of cylinder (given)

⇒ Volume of cylinder = (100/36) × Volume of cube = 100 × 729/36 = 2025 cubic ft

∴ Volume of cylinder = 2025 cubic ft