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If length, breadth and height of a cube is increased by 10%, 20% and 30% respectively, then find the percentage increase in its volume.
- a)71.6%
- b)70%
- c)73.36%
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If length, breadth and height of a cube is increased by 10%, 20% and ...
Let the length, breadth and height (in units) of original cube be x.
∴ Volume of the original cube = x3 New volume = 1.1x × 1.2x × 1.3x = 1.716 x3
∴ Required percentage
= 71.6%
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Community Answer
If length, breadth and height of a cube is increased by 10%, 20% and ...
To find the percentage increase in volume, we need to calculate the initial volume and the final volume after the increase in dimensions. Let's assume the initial length, breadth, and height of the cube are L, B, and H respectively.
Initial Volume of the Cube: L * B * H
Increase in Length: 10% of L = (10/100) * L = 0.1L
Increase in Breadth: 20% of B = (20/100) * B = 0.2B
Increase in Height: 30% of H = (30/100) * H = 0.3H
New Length: L + 0.1L = 1.1L
New Breadth: B + 0.2B = 1.2B
New Height: H + 0.3H = 1.3H
Final Volume of the Cube: (1.1L) * (1.2B) * (1.3H) = 1.716LBH
Percentage Increase in Volume = (Final Volume - Initial Volume) / Initial Volume * 100
= (1.716LBH - LBH) / LBH * 100
= 0.716LBH / LBH * 100
= 71.6%
Therefore, the percentage increase in volume of the cube is 71.6%. Hence, option A is the correct answer.
Initial Volume of the Cube: L * B * H
Increase in Length: 10% of L = (10/100) * L = 0.1L
Increase in Breadth: 20% of B = (20/100) * B = 0.2B
Increase in Height: 30% of H = (30/100) * H = 0.3H
New Length: L + 0.1L = 1.1L
New Breadth: B + 0.2B = 1.2B
New Height: H + 0.3H = 1.3H
Final Volume of the Cube: (1.1L) * (1.2B) * (1.3H) = 1.716LBH
Percentage Increase in Volume = (Final Volume - Initial Volume) / Initial Volume * 100
= (1.716LBH - LBH) / LBH * 100
= 0.716LBH / LBH * 100
= 71.6%
Therefore, the percentage increase in volume of the cube is 71.6%. Hence, option A is the correct answer.
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