18. School Trophy---
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
Suppose the diameter of the hemisphere is 24 cm and total height ofthe trophy is 28 cm.
(a) Find the curve surface area of cylinder.
(1) 1207.90 cm^2
(2) 1206.86 cm^2
(3) 1230.95 cm2
(iv) 1250.50 cm^2
(b) Find the volume of cylinder.
(1) 7250.60 cm^3
(2)7241.14 cm^3
(iii) 7282.50 cm^3
(iv) None of these
(c) Find the curved surface area of the trophy.
(1) 2113^2 cm
(2) 2112^2 cm
(3)2112 cm^2
(4) 2118 cm^2
(d) Find the volume of the trophy.
(1) 10820 cm^3
(2)10825 cm^3
(3) 10816.71 cm^3
(4) None of these
(e) Find the weight of the metal used in making the trophy, if the weight of 1 cm^3 of metal is 1.5 gm.
(1) 16292.57 gm
(2)16320 gm
(3) 16312.5 gm
(4) None of these
Answers
Answer:
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Answer:
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
2
Diameter= 2
24=12cm
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 h2πrh
= 2 \times \frac{22}{7} \times 12 \times 162×
7
22
×12×16
= 1206.857\:cm^21206.857cm
2
≈ \boxed{\bold{1206.86\:cm^2}}
1206.86cm
2
← option (ii)
(b). Finding the Volume of the cylinder:
The volume of the cylinder is,
= \pi r^2 hπr
2
h
= \frac{22}{7} \times 12^2 \times 16
7
22
×12
2
×16
= \boxed{\bold{7241.14\:cm^3}}
7241.14cm
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^22πrh+2πr
2
= 2\pi r(h + r)2πr(h+r)
= 2 \times \frac{22}{7} \times 12 ( 16+ 12)2×
7
22
×12(16+12)
= \boxed{\bold{2112\:cm^2}}
2112cm
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 hπr
2
h + \frac{2}{3} \pi r^3
3
2
πr
3
= 7241.14 + \frac{2}{3} \times \frac{22}{7} \times (12)^37241.14+
3
2
×
7
22
×(12)
3
= 7241.14 + 3620.577241.14+3620.57
= \boxed{\bold{10861.71\:cm^3}}
10861.71cm
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}}
16292.57gm
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Also View:
A trophy awarded to the best student in the class is in the form of a solid cylinder mounted on a solid hemisphere with the same radius and is made from some metal. this trophy is mounted on a wooden cuboids. the diameter of the hemisphere is 21cm and the total height of the trophy is 24.5cm. find the weight of metal of the used in making the trophy, if the weight of 1cm³ of the metal is 1.2g.(use π=227)
A cricket trophy cup is in the shape of the solid cylinder where the diameter of the base is 14cm & height is 15cm. A cricket ball of diameter 7cm is surmounted on it. The total cup is fixed on cuboid of dimensions 14cm*14cm*7cm. find the volume of the trophy along with the base