Question

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

Answer 1

Answer:

90π cm²

Step-by-step 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)= $\pi \times 5^{2} = 25\pi$

∴ Area of circle (B)= $25\pi$

Finding slant height (l)

Formula; $l= \sqrt{r^{2}+h^{2} }$

⇒l = $\sqrt{5^{2}+12^{2} } = \sqrt{25+144 }$

∴ l= $\sqrt{169} = 13\ cm$

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

Surface area of cone= $5\times 13\times \pi + 25\pi$

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

∴ Surface area of cone= 90π cm²