Question

Find the total surface area of the following

cone. Leave your answer in terms of T.
4 cm
3 cm
SA = [?] cm²
π
Hint: Surface Area of a Cone = Tre + B
Where & slant height, and B = area of the base
Enter

Answer 1

Step-by-step explanation:

Surface area of cone = πrl + B

where

• l is slant height
• r is radius of cone
• B is area of the base

First we have to calculate the area of base and Slant height

Area of base = πr² {r = radius = 3 cm}

Area of base = π (3)²

Area of base = 9π

Now,

Slant height (l) = √r² + h²

From the figure h is height i.e 4 cm

`\sf l = √(3^2 + 4^2) \\ \\ \sf l = √(9 + 16) \\ \\ \sf l = 25 \\ \\ \sf l = √(5 * 5) \\ \\ \sf l = 5 cm`

Slant height of cone is 5 cm

now, let's come to the Surface area of cone

Surface area of cone = πrl + B

Plugging in the value of r, l and B

= (π × 3 × 5) + 9π

= 15 π + 9π

= 24π

Hence, Surface area of the cone is 24π cm²