Answer:
SA = 200π cm²
Step-by-step explanation:
The total surface area (SA) of a cone is calculated as
SA = πrl + πr² ( r is the radius and l the slant height )
We require to calculate the slant height l
Using Pythagoras' identity in the right triangle formed by r, h and l
l² = r² + h²
given r = 8 and h = 15 , then
l² = 8² + 15² = 64 + 225 = 289 ( take square root of both sides )
[tex]\sqrt{l^2}[/tex] = [tex]\sqrt{289}[/tex] , then
l = 17
substitute values into the formula for SA
SA = π × 8 × 17 + π × 8²
= 136π + 64π
= 200π cm²
Answer:
The total surface area of the cone is 200 cm².
Step-by-step explanation:
To find the total surface area of a cone, we need to calculate the sum of its lateral surface area and its base area.
SA total = A lateral + A base
SA total = πrl + πr²
Given:
Height of the cone (h) = 15 cm
Radius of the cone (r) = 8 cm
First, let's find the slant height (l) of the cone using the Pythagorean theorem:
l = [tex]\sqrt{r^{2}+h^{2} }[/tex]
l = [tex]\sqrt{8^{2}+15^{2} }[/tex]
l = [tex]\sqrt{64 + 225}[/tex]
l = [tex]\sqrt{289}[/tex]
l = 17 cm
Now, let's find the total surface area of a cone:
SA total = A lateral + A base
SA total = πrl + πr²
SA total = (π x 8 x 17) + (π x 8²)
SA total = 136π + 64π
SA total = 200π cm²
So, the total surface area of the cone is 200 cm².
