Question

A cylindrical road roller made of iron is 1.5 m long. Its inner diameter is 60 cm and the thickness of the iron sheet is 10 cm. Find the weight of the roller, if 1 cc of iron weight is 8 gm.

Answer 1

Given:

A cylindrical road roller made of iron is 1.5 m long.

Its inner diameter is 60 cm and the thickness of the iron sheet is 10 cm.

To find:

The weight of the roller, if 1 cc of iron weight is 8 gm.

Solution:

The height of the iron made cylindrical roller = 1.5 m = 150 cm

The inner diameter of the roller = 60 cm

So, the inner radius, r₁ = $\frac{60}{2}$ = 30 cm

The thickness of the iron sheet = 10 cm

∴ The external radius of the roller, r₂ = 30 + 10 = 40 cm

Now,

The volume of the iron made cylindrical road roller is,

= Volume of a hollow cylinder

= $\pi (r_2^2 - r_1^2)h$

on substituting the values we get

= $\frac{22}{7} \times (40^2 - 30^2)\times 150$

= $\frac{22}{7} \times (1600- 900)\times 150$

= $\frac{22}{7} \times 700\times 150$

= $22 \times 700\times 150$

= $\bold{330000\:cm^3}$

If 1 cm³ of iron weighs 8 gm

Then,

330000 cm³ of iron will weigh = 8 gm/cm³ × 330000 cm³ = 2640000 gm

Thus, the weight of the road roller is → 2640000 gm.

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