Question

A cylinder has a height of 4 m and a radius of 1.5 m. What is the approximate radius of a sphere that has the same surface area as a cylinder?

Answer 1

Answer: 2.0 m

Explanation:

2.0 has the same surface area as the cylinder

Answer 2

Given

A cylinder has a height of 4 m and a radius of 1.5 m. What is the approximate radius of a sphere that has the same surface area as a cylinder?

`\text{surface area of a cylinder= surface of area of sphere}`
`2\pi r(r+h)=4\pi r^2`

Given parameters

`\begin{gathered} 2*\pi*1.5(1.5+4)=4\pi* r^2 \\ 2\pi(5.5)=4\pi r^2 \\ 11\pi=4\pi r^2 \\ \text{divide both sides by 4}\pi \\ (11\pi)/(4\pi)=(4\pi r)/(4\pi)^2 \\ (11)/(4)=r^2 \\ \text{Take the square root of both sides} \\ r=\sqrt[]{(11)/(4)} \\ r=1.6583 \end{gathered}`

The final answer

Option A

`r=1.7m`