Question

The volume of a cylinder closed at one end is 1056cm^2 with height 21cm, find the total surface area

Answer 1

Answer: ≈578 cm²

Explanation:

`V_(cyl)=1056\ cm^3\ \ \ \ H=21\ cm\\V_(cyl)=\pi R^2H\\1056=\pi *R^2*21\\1056=21\pi *R^2\\`

Divide both parts of the equation by 21π:

16=R²

4²=R²

4=R

`S{tot\ sur}=\pi R^2+2\pi RH\\S{tot\ sur}=\pi R*(R+2H)\\S{tot\ sur}=\pi *4*(4+2*21)\\S{tot\ sur}=4\pi *(4+42)\\S{tot\ sur}=4\pi *46\\S{tot\ sur}=184\pi \\S{tot\ sur}\approx578\ cm^2`