Question

A roller pin is made by joining three cylindrical
pieces of wood as shown in the figure. The
diameter of the middle cylinder is 7 cm and
that of each of the side cylinder is 3 cm. Total
length of roller pin is 28 cm and the length of
middle piece is double the length of piece on
either side. Find the cost of painting the roller
pin at the rate of 10 paise per cm​

Answer 1

Given:

A roller pin is made by joining three cylindrical pieces of wood as shown in the figure. The diameter of the middle cylinder is 7 cm and that of each of the side cylinder is 3 cm. The total length of the roller pin is 28 cm and the length of the middle piece is double the length of the piece on either side.

To find:

The cost of painting the roller pin at the rate of 10 paise per cm​

Solution:

The diameter of the middle cylinder = 7 cm

∴ The radius of the middle cylinder = $\frac{7}{2} \:cm$

The diameter of each of the side cylinder = 3 cm

∴ The radius of each of the side cylinder = $\frac{3}{2} \:cm$

The total length of the roller pin = 28 cm

Let "x" be the length of each of the side cylinder.

∴ x + x+ 2x = 28

⇒ 2x + 2x = 28

⇒ 4x = 28

⇒ x = 7 cm ← length of each of the side cylinder

∴ 2x = 2 × 7 = 14 cm ← length of the middle cylinder

The curved surface area of the roller pin is,

= Curved surface area of a cylinder → ($2\pi r h$)

= [CSA of side cylinder] + [CSA of the middle cylinder] + [CSA of side cylinder]

= $[2\times \frac{22}{7} \times \frac{3}{2} \times 7] + [2\times \frac{22}{7} \times \frac{7}{2} \times 14] + [2\times \frac{22}{7} \times \frac{3}{2} \times 7]$

= $[22\times 3] + [22 \times 14] + [22 \times 3]$

= $22\times[ 3 + 14 + 3]$

= $22 \times 20$

= $\bold{440\:cm^2}$

Now,

If the cost of painting 1 cm² of the roller pin = 10 paise = Rs. 0.10

Then,

The cost of painting 440 cm² of the roller pin is,

= 440 cm² × Rs. 0.10

= Rs. 44

Thus, the cost of painting the roller pin at the rate of 10 paise per cm² is → Rs. 44.​

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Answer 2

Answer:

let length of each side of cylinder be x

x+x+2x=28

2x+2x =28

4x+28

x=28/4

x= 7

then 2x= 2×7 =14

Step-by-step explanation:

csa of cylinder 2/rh