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Subject Test Math 1

Question 24 of 32

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SAT Subject Test

The dimensions of a rectangular solid are 3 inches by 4 inches by 5 inches. The length of each edge of the solid is to be increased by 20 percent sign. What is the surface area, in square inches, of the new solid?

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86.4

Correct Answer: 
No

94

Correct Answer: 
No

112.8

Correct Answer: 
No

135.4

Correct Answer: 
Yes

162.4

Correct Answer: 
No

If the length of each edge is increased by 20 percent sign, then the area of each face of the new solid is increased by 44 percent sign (Error converting from MathML to accessible text., where Error converting from MathML to accessible text. and w represent the dimensions of a face). The surface area of the original solid is equal to 2 left square bracket left parenthesis 3 invisible times cross times 4 right parenthesis plus left parenthesis 3 invisible times cross times 5 right parenthesis plus left parenthesis 4 invisible times cross times 5 right parenthesis right square bracket equals 94 square inches. Thus, the surface area of the new solid is equal to 1.44 invisible times cross times 94 invisible times equals 135.36 square inches, which rounds to 135.4. The correct answer is D.

Another way to solve the problem is to find the lengths of each edge of the new solid by multiplying the length of each edge by 1.2 and then compute the surface area. The dimensions of the new solid are 3.6 inches by 4.8 inches by 6 inches, so the surface area is equal to2 left square bracket left parenthesis 3.6 invisible times cross times 4.8 right parenthesis plus left parenthesis 3.6 invisible times cross times 6 right parenthesis plus left parenthesis 4.8 invisible times cross times 6 right parenthesis right square bracket equals 135.36 square inches.

Question Difficulty: 
hard