Question

the perimeter of the circular base of a cone is 132 cm and its vertical height is 28 cm find the curved surface area total surface area and volume of the cone​

Answer 1

i. Curved surface area = 2310
`cm^(2)`

ii. Total surface area = 3696
`cm^(2)`

iii. volume = 12936
`cm^(3)`

Explanation:

Perimeter of the circular base = circumference of the circle = 132 cm

circumference of a circle = 2
`\pi`r

132 = 2
`\pi`r

r =
`(132)/(2\pi )`

=
`(66)/(\pi )`

r = 66 x
`(7)/(22)`

= 3 x 7

= 21

radius = 21 cm

vertical height, h = 28 cm

Thus applying the Pythagoras theorem,

`l^(2)` =
`h^(2)` +
`r^(2)`

=
`28^(2)` +
`21^(2)`

= 784 + 441

= 1225

l =
`√(1225)`

l = 35 cm

The slant height is 35 cm.

i. Curved surface area =
`\pi`rl

=
`(22)/(7)` x 21 x 35

= 22 x 3 x 35

= 2310

curved surface area of the cone is 2310
`cm^(2)`.

ii. Total surface area =
`\pi r^(2)` +
`\pi`rl

=
`\pi`r(r + l)

=
`(22)/(7)` x 21 (21 + 35)

= 22 x 3 x 56

= 3696

The total surface area of the cone is 3696
`cm^(2)`.

iii. volume of a cone =
`(1)/(3)`
`\pi r^(2)`h

=
`(1)/(3)` x
`(22)/(7)` x
`21^(2)` x 28

= 12936

The volume of the cone is 12936
`cm^(3)`