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alexisnichols2001

01.08.2020

Mathematics

The volume of the block is $\frac{15}{512}\ cm^3$ cubic cm. The number of cubic wooden blocks with a side length of 1/8 cm that can be cut from the rectangular block is 15.

Step-by-step explanation:

The volume of a rectangular prism is given by :-

V=lwh

Given: A solid wooden block in the shape of a rectangular prism has a length,width and height of 3/8 cm, 1/8 cm, and 5/8 cm, respectively.

Now, the volume of a wooden block will be :-

$V=\frac{3}{8}\times\frac{1}{8}\times\frac{5}{8}=\frac{15}{512}\ cm^3$

The volume of cubic block with side length of 1/8 cm is given by :-

$V=(side)^3=(1/8)^3=\frac{1}{512}\ cm^3$

Now, the number of cubic wooden blocks with a side length of 1/8 cm that can be cut from the rectangular block is given by :-

$\frac{\text{Volume of wooden block}}{\text{Volume of cubic block}}=\frac{\frac{15}{512}}{\frac{1}{512}}=15$

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