Question

Solve

Solve
a cylinder of radius r cm and height h cm has a curved surface area A cm
`{}^(2)`, where
`A = 2\pi rh.`
a) obtain a formula for h
b) find the value of h when A = 93 ,R = 2.5 and
`\pi`= 3.1​​

Answer 1

A cylinder of radius r cm and height h cm has a curved surface area A cm². Where –

• A = 2πrh cm²

a) We are asked to find formula for h.

`\qquad`
`\purple{ \bf \longrightarrow A=2 \pi rh }`

First, overturn the equation

`\qquad`
`\sf \longrightarrow 2 \pi rh =A`

Divide both sides by 2πr

`\qquad`
`\sf \longrightarrow (2\pi rh)/(2\pi r ) = (A)/(2\pi r)`

`\qquad`
`\sf \longrightarrow \frac{\cancel{2 \pi r }h}{\cancel{2\pi r} } = (A)/(2\pi r)`

`\qquad`
`\purple{\bf \longrightarrow h = (A)/(2 \pi r )}`

b) Again, we are given –

• Curved surface area, A = 93 cm²
• Radius, r = 2.5 cm
• π = 3.1

`\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}`

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

`\qquad`
`\bf \longrightarrow h = (A)/(2\pi r )`

`\qquad`
`\sf \longrightarrow h = (93)/(2 * 3.1 * 2.5 )`

`\qquad`
`\sf \longrightarrow h = (93)/(15.5)`

`\qquad`
`\sf \longrightarrow h =\cancel{ (93)/(15.5)}`

`\qquad`
`\pink{ \bf \longrightarrow h = 6\: cm }`

• Henceforth, height of the cylinder is 6 cm.