Question

Find the total surface area of the following cone. Leave your answer in terms of pi.

Answer 1

S.A. = 90 pi cm2

Explanation:

1. pi(3.14) x radius(5) x slant height(13) = 90

Answer 2

90π cm²

Explanation:

Given: Radius of circular base= 5 cm

height= 12 cm

Now finding the surface of cone.

Formula; Surface area of cone=
`\pi rl+ B`

Where; r= radius

l= slant height

B is the area of base, which is circle.

Area of circle (B)= πr²

Area of circle (B)=
`\pi * 5^(2) = 25\pi`

∴ Area of circle (B)=
`25\pi`

Finding slant height (l)

Formula;
`l= \sqrt{r^(2)+h^(2)  }`

⇒l =
`\sqrt{5^(2)+12^(2)  } = √(25+144 )`

∴ l=
`√(169) = 13\ cm`

Next, using the formula for finding surface area of cone.

Surface area of cone=
`5* 13* \pi + 25\pi`

⇒ Surface area of cone=
`65\pi +25\pi = 90\pi`

∴ Surface area of cone= 90π cm²