Question

Find the total surface area of a cone , if its slant height is 21m and diameter of its base is 24 m .​

Answer 1

Step-by-step explanation:

Given slant hight of cone = 21m

diameter of base 24m or radius =12m

now TSA of cone =πrl+πr2

=πr[r+l]=3.14×12[21+12]

=3.14×12[33]

TSA of cone = 1243.44m2.

Answer 2

Answer:

The total surface area of the cone is approximately 1244.57 m².

Step-by-step-explanation:

We have given that,

The slant height ( l ) of a cone is 21 m.

The diameter of the base of cone ( d ) is 24 m.

We have to find the total surface area of the cone.

Now,

Radius of base of cone is half of the diameter of its base.

$\displaystyle{\therefore\sf\:r\:=\:\dfrac{d}{2}}$

$\displaystyle{\implies\sf\:r\:=\:\cancel{\dfrac{24}{2}}}$

$\displaystyle{\implies\boxed{\red{\sf\:r\:=\:12\:m}}}$

Now, we know that,

$\displaystyle{\pink{\sf\:Total\:surface\:area\:of\:cone\:=\:\pi\:r\:(\:r\:+\:l\:)}\sf\:\quad\:-\:-\:-\:[\:Formula\:]}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{22}{7}\:\times\:12\:(\:12\:+\:21\:)}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{22}{7}\:\times\:12\:\times\:33}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{22\:\times\:12\:\times\:33}{7}}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{264\:\times\:33}{7}}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\cancel{\dfrac{8712}{7}}}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:1244.571}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:Total\:surface\:area\:of\:cone\:\approx\:1244.57\:m^2}}}}$

∴ The total surface area of the cone is approximately 1244.57 m².