An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height be 22 cm, the diameter of the cylindrical portion 8 cm and the diameter of the top of the funnel 18 cm, find the area of the tin required.
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Answer:
The area of tin sheet required to make the oil funnel is 249 π cm²
Step-by-step explanation:
SOLUTION :
Given :
Total height of a oil funnel = 22 cm
Diameter of top of the frustum = 18 cm
Radius of top of the frustum , R = 18/2 = 9 cm
Diameter of bottom of the frustum = 8 cm
Radius of bottom of the frustum and Cylinder , r = 8/2 = 4 cm
Height of cylinder ,h = 10 cm
Height of the frustum, H = Total height of oil funnel – Height of the cylinder = 22 cm – 10 cm = 12 cm
Slant height of the frustum, l= √h² + (R - r)²
= √12² + (9 - 4 )²
= √144 + 5²
= √144 + 25
= √169
= 13 cm
Slant height of the frustum, l = 13 cm
Surface Area of tin sheet required to make the funnel = π(R + r)l + 2πrh
= π(9 + 4) ×13 cm + 2 π × 4× 10
= π(13 × 13 + 80 )
= π (169 + 80 )
= 249 π cm²
Surface Area of tin sheet required to make the funnel = 249 π cm².
Hence, the area of tin sheet required to make the oil funnel is 249 π cm².
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here is ur 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
Thus, the area of tin sheet required to make the oil funnel is 782.6 cm2
hope it helps you...
Please mark as a brainliest ✌❤☺☺❤✌☺❤
here is ur 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
Thus, the area of tin sheet required to make the oil funnel is 782.6 cm2
hope it helps you...
Please mark as a brainliest ✌❤☺☺❤✌☺❤
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