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Question

The length of a cuboid is twice its breadth. The breadth is twice its height. Then, the ratio of LSA to TSA is .

A
3:7
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B
7:2
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C
7:3
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Solution

The correct option is A 3:7
Let, l be the length, b be the breadth and h be the height.

Given, length of the cuboid (l)=2b,
breadth of the cuboid (b)=2h,
Therefore, l=2×2h=4h,
where h is the height of the cuboid.

Lateral surface area
=2(lh+bh)=2(4h×h+2h×h)=12h2

Total surface area
=2(lb+bh+lh)=2(4h×2h+2h×h+4h×h)=28h2

Ratio
=Lateral surface areaTotal surface area=12 h228 h2=37

Therefore, the ratio of LSA to TSA is 3:7.

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