Question

find the surface area of the composite 3D figure below. leave in terms of pi, numerical value only

Answer 1

Given:

The diameter of the cylinder = 34 m

So, the radius (r) = 17 m

The height (h) of the cylinder = 12 m

The slant height (l) of the cone = 20 m

To find the surface area of the given figure.

Surface area of the given fig = surface area of cylinder + surface area of the cone

Formula:

The surface area of the cylinder is $2 \pi r(r+h)$

The surface area of the cone is $\pi rs$

Now,

The surface area of the cylinder is given by

$SA=2 \pi 17(17+12)$

     $=2 \pi 17(29)$

     $=2 \pi (493)$

$SA=986 \pi$

The surface area of the cylinder is 986π m²

The surface area of the cone is given by

$SA=\pi rs$

$SA=\pi (17)(20)$

     $=340 \pi$

Thus, the surface area of the cone is 340π m²

The surface area of the composite figure is given by

Surface area = Surface area of cylinder + Surface area of cone

Substituting the values, we get;

$SA=986\pi +340 \pi=1326 \pi \ m^2$

Thus, the surface area of the composite figure is 1326π m²