A cube is having surface area of 5400 square units. Its volume would increase approximately ______ if the side is increased by 5 units.

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 21 Jun, 2024 Shift 1)

Answer 1

Given:

Surface area of the cube = 5400 square units.

Side increment = 5 units.

Formula Used:

Surface area of a cube = 6a²

Volume of a cube = a³

Calculation:

Let the side of the cube be a units.

Surface area = 6a²

⇒ 6a² = 5400

⇒ a² = 5400 / 6

⇒ a² = 900

⇒ a = 30 units

New side of the cube = a + 5 = 30 + 5 = 35 units

Original volume = a³ = 30³

⇒ 30³ = 27000 cubic units

New volume = (a + 5)³ = 35³

⇒ 35³ = 42875 cubic units

Increase in volume = New volume - Original volume

⇒ Increase in volume = 42875 - 27000

⇒ Increase in volume = 15875 cubic units

Approximate increase in volume = 0.59 × 27000

⇒ 15870 cubic units

The volume would increase approximately 59% .

Download Solution PDF