find the total surface area of a right cone with a base diameter of 10cm and a height of 12cm. give your answer in terms of pie.

The total surface area is 90π cm²

Step-by-step 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