Question

circumference of the base of a cylinder open at the is 132 cm the sum of radius and the height of the cylinder is 41 find the cost of polishing the outer surface of cylinder at the rate of ₹10per square meter​

Answer 1

Answer:

The cost for polishing the outer surface of the cylinder is ₹ 2.640

The cost for polishing the outer surface of the cylinder including the base is ₹ 4.026

Step-by-step explanation:

Circumference = c = 132 cm

Radius (r) + Height (h) = 41 cm

Circumference of the base = c = 2 $\pi$ r

∴ 132 = 2 $\pi$ r

∴ r = 132 / (2 $\pi$ )

∴ r = 66 /  $\pi$

Using  $\pi$ = 22/7

∴ r = 66 / ( 22/7 )

∴ r = (66 x 7) / 22

∴ r = 3 x 7

∴ r = 21 cm

∴ r + h = 41 cm

∴ 21 + h = 41

∴ h = 41 - 21

∴ h = 20 cm

For polishing the outer surface of the cylinder,

Outer surface of the cylinder = 2 $\pi$ r h

= 2 x (22/7) x 21 x 20

= 2 x 22 x 3 x 20

= 2640 cm²

= 0.2640 m²

For 1 m² ≡ ₹ 10

For 0.2640 m² ≡ ₹ y

y = 0.2640 x 10 = ₹ 2.640

For polishing the outer surface of the cylinder including the base,

Outer surface of the cylinder = 2 $\pi$ r h + $\pi$ r²

= 2640 cm² + (22/7) x 21²

= 2640 cm² + 22 x 3 x 21

= 2640 cm² + 1386 cm²

= 4026 cm²

= 0.4026 m²

For 1 m² ≡ ₹ 10

For 0.4026 m² ≡ ₹ z

z = 0.4026 x 10 = ₹ 4.026