Question

Find the lateral area and the surface area of the composite solid. Keep answer in exact form.

Answer 1

Answer:

a) Lateral area of the solid = 2011.43 $cm^{2}$

b) Surface area of the solid = 2544 $cm^{2}$

Step-by-step explanation:

a) Lateral area of the figure = 2$\pi$rh

where; r is the radius of the cylinder, and h is its height.

Lateral area of the figure = 2 x $\frac{22}{7}$ x 10 x 32

                                          = 2011.43 $cm^{2}$

b) The surface area = 2$\pi$r(r + h) - 2($\frac{1}{2}$ x b x h)

                                 = 2$\pi$r(r + h) - (b x h)

The height of the isosceles triangle can be determined by applying the Pythagoras theorem to have,

$10^{2}$ = $6^{2}$ + $h^{2}$

100 = 36 + $h^{2}$

$h^{2}$ = 100 - 36

   = 64

h = $\sqrt{64}$

  = 8

h = 8 cm

The surface area of the solid = 2 x $\frac{22}{7}$ x 10 (10 + 32) - 12 x 8

                                                = 2640 - 96

                                                = 2544

The surface area of the solid is 2544 $cm^{2}$.