Answer:
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](https://tex.z-dn.net/?f=%5Cpi%20rl)
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](https://tex.z-dn.net/?f=%5Cpi%20rl%5C%5C%3D%3E%5Cpi%206%2A8.5%5C%5C%3D%3E%203.14%2A51%5C%5C%3D%3E160.14)
we will use value of
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](https://tex.z-dn.net/?f=%5Cpi%20rl%5C%5C%3D%3E3.14%2A6%2A8.5%5C%5C%3D%3E153)
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](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
Thus area of base is given below
![\pi r^2\\=>3.14*6^2\\=>113.04](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%5C%5C%3D%3E3.14%2A6%5E2%5C%5C%3D%3E113.04)
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.