Answer:
The total surface area is 90π cm²
Explanation:
To find the total surface area of his cone, we will follow the steps below;
write the formula for finding the total surface area of a cone
Total surface area = πrl + πr²
where r is the radius and l is the slant height
from the question, diameter = 10 cm, diameter = 2r this implies that r = d/2 = 10/2 = 5 cm
Also from the question given to us, height h = 12 cm, but what we want is slant height l. We can find this by using the Pythagoras theorem to find the slant height using the height giving to us and the radius.
opposite² + adjacent² = hypotenuse²
where radius is the adjacent, height is the opposite and the slant height is the hypotenuse
5² + 12² = l²
25 + 144 = l²
169 = l²
13 = l
l= 13 cm
hence slant height =13 cm
We can now proceed to insert the values into the formula
Total surface area = πrl + πr²
= π×5×13 + π×5²
=65π + 25π
=90π cm²
The total surface area is 90π cm²