Question

Find the surface area of the cone with a diameter of 12 centimeters and a slant height of

85 millimeters.
Please answer due in 20 minutes

Answer 1

lateral surface area is 160.14 square cm.

Total surface area is 273.16 square cm

Explanation:

Lateral surface area of cone is given by
`\pi rl`

where r is radius of cone

and l is slant height of cone.

l = 85 millimetres

we know that 10 millimetres is equal to 1 cm

Thus 85 millimetres is equal to 8.5 cm

Thus slant height(l) in cm is 8.5
`\pi rl\\=>\pi 6*8.5\\=> 3.14*51\\=>160.14`

we will use value of
`\pi` as 3.14

Diameter of cone = 12 cm

we know that radius is equal to half of Diameter

radius of given cone = 1/2 *Diameter = 1/2 * 12 = 6 cm.

Thus lateral surface area of cone is given by

`\pi rl\\=>3.14*6*8.5\\=>153`

Thus, lateral surface area is 160.14 square cm.

Area of base of cone will be area of circular base

area of circle is given by
`\pi r^2`

Thus area of base is given below

`\pi r^2\\=>3.14*6^2\\=>113.04`

area of base is 113.04 square cm

Total surface area of cone is sum of area of base and lateral surface area

Total surface area = 160.14+113.04 = 273.16 square cm.