Question

Pyramid A is a square pyramid with a base side length of 9 inches and a height of 4 inches. Pyramid B has a volume of 8,100 in3. How many times bigger is the volume of pyramid B than pyramid A?


15
32
54
75

Answer 1

The volume of pyramid B is 75 times bigger than volume of pyramid A [ The correct option is 75 ]

Given :

• Pyramid A is a square pyramid with a base side length of 9 inches and a height of 4 inches.

• Pyramid B has a volume of 8100 in³

To find :

The number of times the volume of pyramid B is bigger than pyramid A is

• 15

• 32

• 54

• 75

Solution :

Step 1 of 2 :

Calculate volume of pyramid A

Pyramid A is a square pyramid with a base side length of 9 inches and a height of 4 inches

The volume of pyramid A

$\displaystyle \sf = \frac{1}{3} \times Base \: area \times Height$

$\displaystyle \sf = \bigg(\frac{1}{3} \times {9}^{2} \times 4\bigg) \: \: {in}^{3}$

$\displaystyle \sf = 108 \: \: {in}^{3}$

Step 2 of 2 :

Calculate number of times the volume of pyramid B is bigger than volume of pyramid A

The number of times the volume of pyramid B is bigger than volume of pyramid A

$\displaystyle \sf = \frac{Volume \: of \: pyramid \: B }{Volume \: of \: pyramid \: A }$

$\displaystyle \sf = \frac{8100}{108}$

$\displaystyle \sf = 75$

Hence the correct option is 75

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