A gulabjamun contains sugar syrup upto about 30% of its volume. Tejinder purchased 28 gulabjamuns. Each gulabjamun is cylindrical in shape having hemispherical ends on both sides. Its height is 5.6 cm and diameter is 1.4 cm. How much sugar syrup did Tejinder get ?
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Step-by-step explanation:
The gulab jamun can be considered as the combination of three solids as shown in the given diagram.
Here, radius of the hemispherical ends = radius of the cylinder (r) = 1.4 cm
Height of the cylindrical part (h) = 5 – (1.4 + 1.4) cm
= 2.2 cm.
∴ Volume of one gulab jamun = 2 × (Volume of hemisphere) + Volume of cylinder
=
2
×
[
2
3
π
r
3
]
2×[23πr3]
+
π
r
2
h
πr2h
=
π
r
2
(
4
3
r
+
h
)
πr2(43r+h)
=
22
7
×
1.4
×
1.4
[
4
3
×
1.4
+
2.2
]
227×1.4×1.4[43×1.4+2.2]
=
22
7
×
14
10
×
14
10
[
4
3
×
14
10
+
22
10
]
227×1410×1410[43×1410+2210]
=
154
25
×
61
15
=
9394
375
c
m
3
15425×6115=9394375cm3
∴ Quantity of syrup found in 45 gulab jamuns
= 30% of
(
45
×
9394
375
)
(45×9394375)
=
3
10
×
310×
(
45
×
9394
375
)
(45×9394375)
= 338.184
≈ 338cm3
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