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# In the below figure, the base of the uniform solid is a right triangle

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Manager
Joined: 14 Mar 2014
Posts: 142
GMAT 1: 710 Q50 V34
In the below figure, the base of the uniform solid is a right triangle  [#permalink]

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13 May 2015, 14:00
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:02) correct 23% (02:38) wrong based on 45 sessions

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In the below figure, the base of the uniform solid is a right triangle with sides of length 3, 4 and 5. If the volume of the solid is 30, what is the total surface area?

30
36
47
60
72
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Re: In the below figure, the base of the uniform solid is a right triangle  [#permalink]

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13 May 2015, 17:34
1
Hi VenoMftw,

To answer this question, we'll need to figure out the height of the shape.

The VOLUME of this 'uniform solid' is (area of the base)(height). Since the base is a right triangle, it's area is...

A = (1/2)(3)(4) = 6

So the volume of the solid is

V = (area of the base)(height)
30 = (6)(H)
30/6 = H
5 = H

Now that we know the height is 5, we can count up the areas of the various surfaces to get the TOTAL surface area.

We already know the area of the "bottom" of the solid (we figured out that it was 6), so that's also the area of the "top" of the solid.

The three 'sides' of the solid are all rectangles with areas of...
(3)(5) = 15
(4)(5) = 20
(5)(5) = 25

So, the TOTAL surface area is 6+6+15+20+25 = 72

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Rich
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Re: In the below figure, the base of the uniform solid is a right triangle   [#permalink] 13 May 2015, 17:34
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