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Oksi-84 [34.3K]
3 years ago
15

A right rectangular prism is packed with cubes of side length 1 over 2 inches. If the prism is packed with 5 cubes along the len

gth, 3 cubes along the width, and 6 cubes along with the height, what is the volume of the prism?
A.Fraction 3 and 3 over 4 cubic inches

B.7 cubic inches

C.Fraction 11 and 1 over 4 cubic inches

D.24 cubic inches
Mathematics
1 answer:
Dmitry [639]3 years ago
5 0

Answer:

<em>Answer: C.Fraction 11 and 1 over 4 cubic inches</em>

Step-by-step explanation:

The volume of a rectangular prism of length L, width W, and height H is given by:

V=LWH

The prism is packed with cubes of a side length of a=1/2 inch. The volume of each cube is:

V_c=a^3=\left(\frac{1}{2}\right)^3=\frac{1}{8}\ in^3

The prism is packed with L=5, W=3, and H=6, thus the volume (in cubes) is:

V=5*3*6=90\ cubes

Since each cube has a volume of \frac{1}{8} in^3:

V=90\cdot\frac{1}{8}=\frac{45}{4}

Expressing as a mixed fraction:

V=\frac{45}{4}=\frac{44+1}{4}=11\frac{1}{4}

Answer: C.Fraction 11 and 1 over 4 cubic inches

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