Question

Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 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.

Answer 1

Given↷

• Base length of pyramidA⇢14inches
• Height of pyramidA⇢6inches
• volume of pyramidB⇢ 3,146 in³

To find ↷

• Measure of pyramid B as compared to pyramid A

Answer ↷

• 800%

Solution ↷

We know that,

volume of a square pyramid is base length squared times one third height of the pyramid

so,

$\huge v = a {}^{2} \frac{h}{3}$

• v - volume
• a - base length
• h - height

inserting the values given in term of pyramidA

$\huge v \small {}^{1}\huge= 14 {}^{2} \times \frac{6}{3}$

$\huge v \small {}^{1}\huge= 196 \times 2$

$\huge v \small {}^{1} \huge = 392\small {in}^{3}$

Now, to find how much bigger the pyramid B's volume is as compared to pyramid A ,we'll divide the volume of pyramid B from pyramid A,

$\rightarrow \: \frac{\huge v \small {}^{2}\huge}{\huge v \small {}^{1}\huge}$

$\rightarrow\frac{\huge 3,136\small {in}^{3}}{\huge 392\small {in}^{3}}$

$\rightarrow \huge\: 8$

Hence , pyramid B is 8 times greater than Pyramid A

and to find how much greater pyramid B is as compared to pyramid A,

we'll multiply the times pyramid B is greater than Pyramid A from 100 as one times greater = 100%

hence,

$\rightarrow\: 8 \: times \: greater = 8 \times 100\%$

$\rightarrow\: 8 \: times \: greater \: = 800\%$

Answer 2

Pyramid A:-

• Base=14in
• Area of base=14²=196in²
• Height=6in

Now

• Volume=Area of base×Height/3
• Volume=196(6/3)
• Volume=196(2)=392in³

Now

No of times bigger:-

• 3136÷392
• 8times