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 [tex]\pi rl[/tex]
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[tex]\pi rl\\=>\pi 6*8.5\\=> 3.14*51\\=>160.14[/tex]
we will use value of [tex]\pi[/tex] 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
[tex]\pi rl\\=>3.14*6*8.5\\=>153[/tex]
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 [tex]\pi r^2[/tex]
Thus area of base is given below
[tex]\pi r^2\\=>3.14*6^2\\=>113.04[/tex]
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.