Question

Diameter of a cone base is 5 cm and a slant height is 4M find surface area

Answer 1

Hi there!

The total surface area (tsa) of a cone can be calculated with this formula :

TSA = ($\pi$ × r × slant height) + $\pi$ × r²

The "r" stands for "radius". The radius is equal to half the diameter, so in order to be able to use the formula, you'll need to divide the diameter by 2 to find the radius :

5 ÷ 2 = 2.5 = radius

Since the slang height is in meters, you'll need to transform it into centimeters in order to have both values in centimeters. To do so you'll need to use the cross product method :

1 m = 100 cm

4 m = x cm

(100 × 4) ÷ 1 = x cm

400 ÷ 1 = x cm

400 = x cm → The slant height is 400cm.

Now replace all the information in the formula and calculate everything :

TSA = ($\pi$ × 2.5 × 400) + ($\pi$ × 2.5²)

TSA = ($\pi$ × 1,000) + ($\pi$ × 6.25)

TSA ≅ 3,141.59 + 19.63

TSA ≅ 3,161.22 cm²

There you go! I really hope this helped, if there's anything just let me know! :)