The square pyramid has a volume of 27 cubic inches. What is the value of X?

Mathematics

1 answer:

wolverine [178]3 years ago

5 0

Answer:

9 inches

Step-by-step explanation:

base is rectangular in shape

Side of base of square pyramid is X inches

height of square pyramid is 1/9 X

Volume of any pyramid is 1/3 *(area of base* height of pyramid)

area of base of square pyramid = Side of base * Side of base

as area of square is equal to side * side

area of base of square pyramid = x* x square inches = $x^2 sq.\ inches$

Volume of pyramid = 1/3 *(area of base* height of pyramid)

substituting given value of of volume of pyramid , height of pyramid and area of base calculated above we have

$27 = 1/3(x^2)*(1/9 x)\\\\27*3*9 = x^3\\729 = x^3\\x = \sqrt[3]{729} \\x = 9$

Therefor value of x is 9 inches.

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Answer:

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Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two pyramids.

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$\dfrac{A_{1}}{ A_{2}} = C^{2}\\\\\dfrac{\text{327 m}^{2}}{A_{2}} = \left (\dfrac{1}{\frac{2}{3}}\right)^{2}\\\\ \dfrac{\text{327 m}^{2}}{A_{2}}= \dfrac{9}{4}\\\\\text{1308 m}^{2}= 9A_{2}\\\\A_{2} = \text{145.33 m}^{2}\\\text{The surface area of the smaller pyramid is \boxed{\text{145.33 m}^{2}}}$