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

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
In the figure above, the base of the uniform solid is a right triangle  [#permalink]

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29 Dec 2015, 07:55
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Difficulty:

35% (medium)

Question Stats:

69% (02:09) correct 31% (02:26) wrong based on 154 sessions

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

A. 30
B. 36
C. 47
D. 60
E. 72

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2015-12-29_1853.png [ 10.47 KiB | Viewed 2959 times ]

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Re: In the figure above, the base of the uniform solid is a right triangle  [#permalink]

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29 Dec 2015, 11:04
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[quote="Bunuel"]
In the figure above, the base of the uniform solid is a right triangle with sides of lengths 3, 4, and 5. If the volume of the solid is 30, what is the total surface area?

volume=30=1/2 * 3*4*h
h=5

SA= 1/2 *3*4*2 + 3*5 + 5*4 + 5*5
SA=72

E. 72
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Re: In the figure above, the base of the uniform solid is a right triangle  [#permalink]

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02 Jan 2016, 18:40
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1
Hi All,

This question is built around a series of standard Geometry Formulas. As long as you keep track of the 'steps' involved, you'll find the math to be fairly straight-forward. Here are some 'hints' to help you get through it in an organized fashion.

1) Volume of any 'uniform solid' is... V = (area of the 'base')(height). Using this formula, you can find the height of the solid in this question.
2) We're asked for the SURFACE AREA of this solid, so we need the individual areas of ALL 5 sides...
3) The area of the 'bottom' and 'top' are the same triangle (we're told that it's a RIGHT TRIANGLE, so you can figure out it's area using A = (1/2)(length)(width)).
4) The areas of the three 'sides' are 3 different rectangles (and each has an area of A = (base)(height).
5) Finally, just add up all 5 areas and you'll have the Total Surface Area.

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Re: In the figure above, the base of the uniform solid is a right triangle  [#permalink]

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30 Apr 2017, 14:40
Volume = Area of Base * height
30 = (3*4)/2 * h
h = 5

Using this information and the sides given in the figure:
Area of base and top = 6+6 = 12
Area of 5x4 side = 20
Area of 5x3 side = 15
Area of 5x5 side = 25
Total Surface Area = 12+20+15+25 = 72
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Re: In the figure above, the base of the uniform solid is a right triangle  [#permalink]

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25 Nov 2018, 06:18
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Re: In the figure above, the base of the uniform solid is a right triangle   [#permalink] 25 Nov 2018, 06:18
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# In the figure above, the base of the uniform solid is a right triangle

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