Mathematics: 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

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Find the surface area of the cone with a diameter

jfkdhrmd

27.01.2022

lateral surface area is 160.14 square cm.

Total surface area is 273.16 square cm

Step-by-step 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.

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