Question

Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750n. What is the percentage change in volume between cylinders A and B? Cylinder B is 50% smaller than cylinder A. Cylinder B is 75% smaller than cylinder A Cylinder B is 50% bigger than cylinder A Cylinder B is 200% bigger than cylinder A

Answer 1

Cylinder B is 50% bigger than Cylinder A

Explanation:

`\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

Cylinder A

Given:

• r = 10 in
• h = 5 in

Substituting the given values into the formula:

`\implies \sf Volume_A=\pi (10)^2(5)=500\pi \:in^3`

Cylinder B

Given:

• volume = 750 in³

`\implies \sf Volume_B=750\pi \:in^3`

Percentage Change

`\begin{aligned}\sf percentage\:change & =\sf (final\:value-initial\:value)/(initial\:value) * 100\\\\& = \sf (Volume_B-Volume_A)/(Volume_A) * 100\\\\& = \sf (750\pi-500\pi)/(500\pi) * 100\\\\& = \sf (1)/(2) * 100\\\\& = \sf 50\%\end{aligned}`

Therefore, Cylinder B is 50% bigger than Cylinder A

Answer 2

Answer: Cylinder B is 50% bigger than cylinder A

Cylinder A volume:

= πr²h

= π(10)²(5)

= 500π

Cylinder B volume:

= 750π

Cylinder B bigger than Cylinder A by:

= (750π - 500π)/500π × 100 = 50%

`\hrulefill`

Hence, cylinder B is bigger than cylinder A by 50%