Chapter ISG, Problem 2.7.5P

To determine

The formula of the surface area is $s=2\pi rh+2\pi r^2$ ,Find the height and radius

Answer to Problem 2.7.5P

  $h=5cm$

  $r=3.5cm$

Explanation of Solution

Given information:

The surface area $(s)=72\pi c{m}^3$

Radius = $4cm$

Formula used:

  $s=2\pi rh+2\pi r^2$

Calculation:

  $s=2\pi rh+2\pi r^2$

Arrange the term

  $2\pi rh=s-2\pi r^2$

Equation for h

  $h=\left(s-2\pi r^2\right)÷2\pi r$

Put the value

  $h=\left(72\pi -2\pi 4^2\right)÷2\pi \left(4\right)$

Solve the bracket term

  $h=\left(72\pi -32\pi \right)÷2\pi \left(4\right)$

To subtact the bracket term

  $h=\left(40\pi \right)÷8\pi$

Hence, On dividing the final answer is-

  $h=5cm$

Given information:

The Lateral surface area of cylinder $\left(L\right)=2\pi rh$

Height = $7.5cm$

Lateral area = $52.5\pi$

Formula used:

  $l=2\pi rh$

Calculation:

  $l=2\pi rh$

Equation for r

  $r=l÷2\pi h$

Put the value of l and h

  $r=52.5\pi ÷2\pi \left(7.5\right)$

To sove the bracket term

  $r=52.5\pi ÷15\pi$

Hence, On dividing the final answer is-

  $r=3.5cm$