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# A rectangular solid has a square base and altitude of 7. If the volume

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A rectangular solid has a square base and altitude of 7. If the volume  [#permalink]

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09 Jul 2018, 06:17
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15% (low)

Question Stats:

80% (01:13) correct 20% (01:37) wrong based on 25 sessions

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A rectangular solid has a square base and altitude of 7. If the volume of the solid is 252, then the perimeter of the square base is

(A) 9
(B) 24
(C) 28
(D) 36
(E) 49

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A rectangular solid has a square base and altitude of 7. If the volume  [#permalink]

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09 Jul 2018, 06:29
Rectangular solid has a square base. Let say the side of square is 'a'

Altitude of the solid is 7

Volume of the solid is $$a^2 * 7 = 252$$

=> $$a^2 = 36$$

=> $$a = 6$$ (since length cannot be negative, we can ignore a being -6)

Perimeter of square base = $$4 * a = 4 * 6 = 24$$

hence option B
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Re: A rectangular solid has a square base and altitude of 7. If the volume  [#permalink]

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09 Jul 2018, 06:33
Bunuel wrote:
A rectangular solid has a square base and altitude of 7. If the volume of the solid is 252, then the perimeter of the square base is

(A) 9
(B) 24
(C) 28
(D) 36
(E) 49

$$7a^2 = 252$$

Or, $$a = \sqrt{36}$$

So, $$a = 6$$

Hence perimeter is 4*6 = 24, Answer must be (B)
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Re: A rectangular solid has a square base and altitude of 7. If the volume  [#permalink]

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09 Jul 2018, 06:41

Solution

Given:
• A rectangular solid has a square base and altitude of 7
• The volume of the solid is 252

To find:
• The perimeter of the square base

Approach and Working:
Let us assume the length of each side of the square base is x
The volume of the solid = area of the base * height = $$x^2 * 7 = 252$$
• Therefore, $$x^2 = 36$$
Or, x = 6

• Then, the perimeter of the square base = 6 * 4 = 24

Hence, the correct answer is option B.

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Re: A rectangular solid has a square base and altitude of 7. If the volume &nbs [#permalink] 09 Jul 2018, 06:41
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