Question

if the diameter and height of a cone are 10 cm and 12 CM then the total surface area of the cone is​

Answer 1

$<h3> !!! given :- diameter of the cone = 10cm therefore it's radius = 10/2 (since we know that diameter is double the Length of radius) = 5cm height = 12cm formula to find the TSA of a cone is πrl + πr² where 'l' is the slant height of the cone. here we are given, the Length of diameter and radius only. so first of all, we need to find it's slant height. by Pythagoras theorem we get, => l = √(r² + h²) (l = hypotenuse, r = base and h = perpendicular) => l = √(5² + 12²) => l = √(25 + 144) => l = √169 => l = 13cm hence, the slant height of the cone is 13cm. now, TSA of the cone = πrl + πr² = (22/7 × 5 × 13 ) + (22/7 × 5 × 5) = 1430/7 + 550/7 = 1980/7 = 282.85cm² (approx.) !!! </h3>$

Answer 2

d=10

r = 10/2=5

h=12

l=?

l^2 = √r^2-h^2

l^2= √5^2-12^2

l^2= √25-144

l = √169

l= 13

total surface area of cone = πrl+πr^2

22/7*13+22/7*(5)^2

1430/7+550/7
=1980/7
=282.85

hope it helps.....