If the slant height of the frustum of a cone is 6 cm and the perimeters of its circular bases are 24 cm and 12 cm respectively. What is the curved surface area of the frustum?
Answers
Answer:
The Curved surface area of the frustum is 108 cm².
Step-by-step explanation:
Given :
Slant height of the frustum of a cone, l = 6 cm
Perimeter of its circular ends are (2πr1) = 24 cm and (2πr2) = 12 cm
Let ‘r1’ and ‘r2’ be the radius of the bottom and top of the circle.
Circumference (Perimeter) of Bottom of circle = 2πr1
24 = 2πr1
πr1 = 24/2 = 12
πr1 = 12 cm……………(1)
Circumference (Perimeter) of top of circle = 2πr2
12 = 2πr2
πr2 = 12/2 = 6
πr2 = 6 cm…………..(2)
Curved surface area of the frustum = (πr1 + πr2)l
= (12 + 6) × 6
= 18 × 6 = 108 cm ²
Curved surface area of the frustum = 108 cm²
Hence, the Curved surface area of the frustum is 108 cm².
HOPE THIS ANSWER WILL HELP YOU….
Slant height of the frustum of cone(l)= 6cm
Perimetres of two circular bases= pm1= 24cm, pm2= 12cm
Radius of 1st circular base(r1):
Pm of 1st circular base= 2pir1= 24cm
=> r1=42/11 cm......
Radius of 2nd circular base9r2):
Pm of 2nd base= 2pir2= 12cm
=> r2= 21/11cm........
C.S.A(frustum of a cone)= pi l(r1+r2)
=> 22/7*6(42/11+21/11)
=> 22/7*6*63/11
=> 108 cm^2..................