Question

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

10 cm
12 cm
1
1
1
1
32 cm
10 cm
Lateral Area
Surface Area

Answer 1

a) Lateral area of the solid = 2011.43
`cm^(2)`

b) Surface area of the solid = 2544
`cm^(2)`

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
`(22)/(7)` x 10 x 32

= 2011.43
`cm^(2)`

b) The surface area = 2
`\pi`r(r + h) - 2(
`(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 =
`√(64)`

= 8

h = 8 cm

The surface area of the solid = 2 x
`(22)/(7)` x 10 (10 + 32) - 12 x 8

= 2640 - 96

= 2544

The surface area of the solid is 2544
`cm^(2)`.