Question

c) An artisan makes the prayer wheel from metal sheet.
Hollow Cylindrical part of diameter 6cm and height 7cm is
covered by two circular metal plates of diameter 6.3cm at
base and top. Spindle on which the cylinder rotates is covered
on top by a circular plate of diameter 2.8cm which is mounted
by an open hemisphere of diameter 2.8cm and cone of same
radius and height 2.1cm. Base of spindle is covered by a
cylindrical wooden handle of radius 1cm and length 10cm. A
small metallic ball of radius 6mm is attached by a chain.
i) Find the area of metal sheet required to make the wheel ii) calculate the volume of wood required to construct the handel
iii.) find the volume of matallic ball of 6mm attached to the cylinder chain. ​

Answer 1

Refer the attachment ↗️↗️

Answer 600 cm ✔️✔️✔️

Answer 2

Concept:

The volume of the sphere, V = 4/3πR³

where R is the radius of the sphere.

Given:

Data for making a prayer wheel is given.

Find:

The area of metal sheet required to make the wheel, the volume of wood required to construct the handle, and the volume of the metallic ball.

Solution:

(i) Area of the metal used,

The spindle, the hollow cylinder, their bases, and the small ball are made of metal, so, the surface areas are added to get the metal sheet required.

Area of metal sheet = Area of spindle + Area of hollow cylinder + Area of bases + Area of the small ball

Area of metal sheet = Area of hemisphere + Area of cone + + Area of hollow cylinder + Area of bases + Area of the small ball

Area of metal sheet = 2π(1.4 cm)² + [ π×1.4 (√1.4²+2.1² )cm²] + 2π(3 cm)(7 cm) + 2π(3 cm)² + 4π(0.6)² cm²

Area of metal sheet = (3.92 + 3.53 + 42 + 18 + 1.44) π cm²

Area of metal sheet = (68.89) π cm²

Area of metal sheet = 216.42 cm²

Hence, the area of the metal sheet required to make the prayer wheel is  216.42 cm².

(ii) Volume of the wood required,

The volume of the cylinder, V = πr²h

V = π( 1 )² × 10

V = 10π

V = 31.42 cm³

Hence, the volume of the wooden handle is 31.42 cm³.

(iii) Volume of the metallic ball,

Given, that the radius of the metallic ball is 6 mm.

V = 4/3πR³

V = 4/3π(0.006)³

V = 904.78 mm³

Hence, the volume of the metallic ball of radius 6 mm is 904.78 mm³.

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