Each side of a cube is increased by x cm, such that its total surface

1.	Each side of a cube is increased by x cm, such that its total surface area is increased by 69%, then find the percentage change in its volume?1. 72.8%2. 119.7%3. 123.3%4. 87.5%
Answer» Correct Answer - Option 2 : 119.7% Given: When each side of a cube increased by 'x' cm then the total surface area is increased by 69%. Concept: Total surface area of the cube = 6 × a2 Volume of the cube = a3 Where a = side Calculation: TSA1/TSA2 = (6 × a2)/[6 × (a + x)2] According to the question, a2/(a + x)2 = 100/169 ⇒ a/(a + x) = 10/13 ⇒ 13a = 10a + 10x ⇒ 3a = 10x ⇒ a/x = 10/3 V1/V2 = a3/(a + x)3 ⇒ 103/133 = 1000/2197 % increase = (1197/1000) × 100 = 119.7% ∴ % increase of the volume is 119.7%. Shortcut: Given: When each side of a cube increased 'x' cm, the total surface area is increased by 69%. Concept: The total surface area of the cube = 6 × a2 The volume of the cube = a3 Where a = side Explanation: TSA → 100 : 169 Side → 10 : 13 Volume → 1000 : 2197 % increase = (1197/1000) × 100 = 119.7%

Each side of a cube is increased by x cm, such that its total surface area is increased by 69%, then find the percentage change in its volume?1. 72.8%2. 119.7%3. 123.3%4. 87.5%

Answer» Correct Answer - Option 2 : 119.7%

Given:

When each side of a cube increased by 'x' cm then the total surface area is increased by 69%.

Concept:

Total surface area of the cube = 6 × a2

Volume of the cube = a3

Where a = side

Calculation:

TSA1/TSA2 = (6 × a2)/[6 × (a + x)2]

According to the question,

a2/(a + x)2 = 100/169

⇒ a/(a + x) = 10/13

⇒ 13a = 10a + 10x

⇒ 3a = 10x

⇒ a/x = 10/3

V1/V2 = a3/(a + x)3

⇒ 103/133 = 1000/2197

% increase = (1197/1000) × 100 = 119.7%

∴ % increase of the volume is 119.7%.

Shortcut:

Given:

When each side of a cube increased 'x' cm, the total surface area is increased by 69%.

Concept:

The total surface area of the cube = 6 × a2

The volume of the cube = a3

Where a = side

Explanation:

TSA → 100 : 169

Side → 10 : 13

Volume → 1000 : 2197

% increase = (1197/1000) × 100 = 119.7%