A metal Chimney consists of of a cylinder portion 20 cm long added to a frustum of a cone if the total height be 40 cm and diameter of the cylinder portion is 14 cm and the diameter of the top of chimney is 24 cm find the area of total required to make chimney Pi is equal to 3.14 and root 17 is equal to 4.12 please give answer
Answers
ANSWER.
Let r 1 and r 2 ( r 1 > r 2) be the radii of ends of the frustum of a cone.
Suppose l, h and H be the slant height of the frustum, height of the frustum and height of the cylinder respectively.
Diameter of top of the frustum, 2r 1 = 18 cm
∴ r 1 = 9 cm.
Diameter of bottom of the frustum, 2r 2 = 8 cm
∴ r 2 = 4 cm
Height of the frustum = Total height of funnel – Height of the cylinder = 22 cm – 10 cm = 12 cm
Slant height of the frustum, l
= h 2 + ( r 1 - r 2 ) 2
= (12 cm) 2 + (9 cm - 4 cm) 2
= 144 cm 2 + 25 cm 2
= 169 cm 2
= 13 cm
Curved surface area of the oil funnel = π( r 1 + r 2)l + 2πr 2H
∴ Area of tin sheet required to make the funnel
= π( r 1 + r 2)l + 2πr 2 H
= 22 7 (9 cm + 4 cm) × 13 cm + 2 × 22 7 × 4 cm × 10 cm
= 22 7 (13 × 13 cm 2 + 80 cm 2 )
= 22 7 × ( 169 cm 2 + 80 cm 2 )
= 22 7 × 249 cm 2
= 782.6 m 2