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Pyramid A is a square pyramid with a base side length of 18 inches and a height of 9 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Provide an explanation and proof for your answer to receive full credit.

Respuesta :

The volume of the pyramid B is 322.63% approx of the volume of the pyramid A.

How to find the volume of a square based right pyramid?

Supposing that:

  • The length of the sides of the square base the pyramid has = b units
  • The height of the considered square based pyramid = h units,

Then, its volume is given by:
[tex]V = \dfrac{1}{3} \times b^2 \times h \: \rm unit^3[/tex]

How to find how much percent 'a' is of 'b'?

  • Suppose a number is 'a'
  • Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

We're given that:

  • For Pyramid A:
  1. Base length = 18 inches
  2. Height = 9 inches

Therefore, we get:

[tex]V = \dfrac{1}{3} \times b^2 \times h \: \rm unit^3\\V= \dfrac{1}{3} \times (18)^2 \times 9 = 972 \: \rm in^3[/tex]

  • For Pyramid B:

Volume of Pyramid B = 3,136 cubic inches

To get the percentage which B is of A in terms of volume of A (as we're comparing the volume of B with A), we get:

[tex]\dfrac{3136}{972} \times 100 \approx 322.63\%[/tex]

Thus, the volume of the pyramid B is 322.63% approx of the volume of the pyramid A.

Learn more about percent here:

https://brainly.com/question/11549320

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