Question

The surface area of the six faces of a rectangular solid are 4, 4, 8, 8, 18 and 18 sq. cm. Find the

volume of the solid.

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Answer 1

Answer:

24$cm^{3}$

Step-by-step explanation:

*rectangular prisms have 3 unique edges

*multiplying those 3 edges gets us the volume

*lets call those 3 edges 'a', 'b', and 'c'

*multiplying any two edges gets us the surface area of one of the faces of the rectangular prism

*we can make 3 equations using this information

1) a x b = 4$cm^{2}$

2) b x c = 8$cm^{2}$

3) a x c = 18$cm^{2}$

*solve for 'b' in equation 1

$b=\frac{4}{a}$

*substitute 'b' in equation 2 with what we just found

$\frac{4}{a} *c=8$

*now solve for 'c' in equation 2

$c=\frac{2}{a}$

*substitute 'c' in equation 3 with what we just found

$a*2a=18$

*now solve for 'a' in equation 3

$a=3cm$

*use this to solve for 'b' and 'c'

$b=\frac{4}{3}cm$

$c=6cm$

*now just multiply all the edges together to find the volume

$a*b*c=3cm*\frac{4}{3}cm*6cm=24cm^{3}$