Mathematics: If 8 times a number is decreased by 20,the result is the same as 3 times the number increased by 80

If 8 times a number is decreased by 20,the result

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15.02.2020

we know that

$scale \ factor^{3}=\frac {volume\ larger\ solid }{volume\ smaller\ solid}$

Find the value of the scale factor

$volume\ larger\ solid= 1,680\ m^{3} \\ volume\ smaller\ solid= 210\ m^{3}$

substitute the values in the formula

$scale \ factor^{3}=\frac {1,680 }{210}$

$scale \ factor^{3}=8$

$scale \ factor=\sqrt[3]{8} \\ scale \ factor= 2$

Find the surface area of the smaller solid

we know that

$scale \ factor^{2}=\frac {surface\ area\ larger\ solid }{surface\ area\ smaller\ solid}$

$surface\ area\ larger\ solid =856\ m^{2} \\ scale\ factor =2$

$surface\ area\ smaller\ solid= \frac{surface\ area\ larger\ solid}{scale \ factor^{2}}$

substitute the values

$surface\ area\ smaller\ solid= \frac{856}{2^{2}}$

$surface\ area\ smaller\ solid=214\ m^{2} }$

therefore

the answer is

The surface area of the smaller solid is equal to $214\ m^{2}$

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