Question

The circumference of the base of a 16 m high solid cone is 33 m. Find the surface area of the cone

Answer 1

this is your answer
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Answer 2

Total Surface Area of Cone is 364.15 sq.m.

Step-by-step explanation:

Given:

Circumference of the base of cone = 33 m

Height of the cone 'h' = 16 m

We need to Surface area of cone.

Solution:

First we will find the radius of Circle.

Now we know that Circumference of circle is 2 times π times radius 'r'.

framing in equation form we get;

$2\pi r=33\\\\r= \frac{33}{2\pi} = 5.25\ m$

Radius of the circle 'r' = 5.25 m

Now we will find the slant height of the cone.

Slant height  $l^2= h^2+r^2 = 16^2+5.25^2 = 256+27.5625 = 283.56$

Taking square root on both side we get;

$\sqrt{l^2}=\sqrt{283.56}  \\\\l = 16.84\ m$

Now We know that Total Surface area of the cone formula is given below;

Total Surface area of the cone = $\pi r(r+l)$

Substituting the values we get;

Total Surface area of the cone = $\pi \times 5.25 (5.25+16.84) = 364.15 \ m^2$

Hence Total Surface Area of Cone is 364.15 sq.m.