The dimensions of a rectangular metal box are 3cm, 5cm, and 8 cm. If the first two dimensions are increased by the same number of centimeters, while the third dimension remains the same, the new volume is 34 3 more than the original volume. What is the new dimension of the enlarged rectangular metal box?
A. 1/2 increment
B. 1/4 increment
C. 1/8 increment
D. 1/16 Increment
A. 1/2 increment
B. 1/4 increment
C. 1/8 increment
D. 1/16 Increment
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Answer:
Old volume= (3cm)(5cm)(8cm) = 120cm³
New volume = 120 + 72 = 192cm³
(x+3)(x+5)(8) = 192
[(x+3)(x+5)(8)]/8 = 192/8
(x+3)(x+5) = 24
x² + 8x + 15 = 24
x² + 8x + 15 - 24 = 0
x² + 8x - 9 = 0
(x+9)(x-1) = 0
x = -9 ; x = 1
choose x = 1 to substitute since is positive because it says that the dimensions increase not decrease
New dimension= (1+3)(1+5)(8) = 4cm by 6cm by 8cm
1.C
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