Question

A school decide to give a trophy of the best student in the class, which is the

form of cylinder mounted on a solid hemisphere with the same radius and is

made from some metal. This trophy is mounted on a wooden cuboid as shown

in the figure.

Suppose the diameter of the hemisphere is 24cm and total height of the

trophy is 28cm.

a) Find the curve surface area of cylinder.

i) 1207.90 cm2

ii) 1206.86 cm2

iii) 1230.95 cm2

iv) 1250.50 cm2

b) Find the volume of cylinder.

i) 7250.60 cm3

ii) 7241.14 cm3

iii) 7282.50 cm3

iv) None of these

c) Find the curved surface area of the trophy.

i) 2113 cm2

ii) 2112 cm2

iii) 2115 cm2

iv) 2118 cm2

d) Find the volume of the trophy.

i) 10820 cm3

ii) 10825 cm3

iii) 10816.71 cm3

iv) None of these

e) Find the weight of the metal used in making the trophy, if the weight of 1cm3 of metal is

1.5gm.

i) 16292.57 gm ii) 16320 gm iii) 16312.5 gm iv) None of these
​

Answer 1

Given:

A school decided to give a trophy of the best student in the class, which is the  form of a cylinder mounted on a solid hemisphere with the same radius and is  made from some metal.

The diameter of the hemisphere is 24cm and the total height of the  trophy is 28cm.

To find:

(a) Find the curved surface area of the cylinder?

(b) Find the volume of the cylinder?

(c) Find the curved surface area of the trophy?

(d) Find the volume of the trophy?

(e) Find the weight of the metal used in making the trophy, if the weight of 1cm3 of metal is  1.5gm?

Solution:

The radius of the hemisphere, r = $\frac{Diameter}{2} = \frac{24}{2} = 12\:cm$

The height of the cylinder "h" is,

= Total height of the trophy - Radius of the hemisphere

= 28 - 12

= 16 cm

(a). Finding the CSA of the cylinder:

The curved surface area of the cylinder is,

= $2\pi r h$

= $2 \times \frac{22}{7} \times 12 \times 16$

= $1206.857\:cm^2$

≈ $\boxed{\bold{1206.86\:cm^2}}$ ← option (ii)

(b). Finding the Volume of the cylinder:

The volume of the cylinder is,

= $\pi r^2 h$

= $\frac{22}{7} \times 12^2 \times 16$

= $\boxed{\bold{7241.14\:cm^3}}$ ← option (ii)

(c). Finding the CSA of the trophy:

The curved surface area of the trophy is,

= CSA of cylinder + CSA of the hemisphere

= $2\pi r h + 2\pi r^2$

=  $2\pi r(h + r)$

= $2 \times \frac{22}{7} \times 12 ( 16+ 12)$

= $\boxed{\bold{2112\:cm^2}}$ ← option (ii)

(d). Finding the Volume of the trophy:

The volume of the trophy is,

= Volume of cylinder + Volume of the hemisphere

= $\pi r^2 h$ + $\frac{2}{3} \pi r^3$

= $7241.14 + \frac{2}{3} \times \frac{22}{7} \times (12)^3$

= $7241.14 + 3620.57$

= $\boxed{\bold{10861.71\:cm^3}}$ ← option (iii)

(e). Finding the weight of the metal used:

If the weight of 1 cm³ of metal = 1.5 gm

Then, the weight of 10861.71 cm³ of metal = 1.5 × 10861.71 = 16292.57 gm

Thus, the weight of the metal used in making the trophy is → option (i) → $\boxed{\bold{16292.57 \:gm}}$

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Also View:

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Answer 2

Step-by-step explanation:

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