Question

Calculate the total surface area of a cone of height 12cm and base radius 5cm. Take π=22/7..?

Answer 1

`282 6/7 cm^2`

Explanation:

The total surface area of a cone is the sum of the area of the base and the lateral area:

`SA=pir^2+pirs`

Where:

r = radius
s= slant height

To find the slant height consider the right triangle formed by the radius(base), the height(vertical leg) then the slant height is the hypotenuse so:
`s^2=r^2+h^2=5^2+12^2=169`
`s=13cm`
Thus:
`SA=22/7(25+5*13)=1980/7=282 6/7 cm^2`

Answer 2

`color(violet)(T S A =282 (6/7)cm^2`

Explanation:

`"Cone Total surface area " T S A = (1/2) (2pir) * h_s + pi r^2`

`r = 5 cm, h = 12 cm, h_s = sqrt(5^2 + 12^2) = 13 cm`

`color(violet)(T S A = pi * 5 * 13 + pi 5^2 = 90pi = 1980/7 = 282 (6/7)cm^2`