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An ice-cream seller sells his ice-creams in two
ways:
Type 1, in a cone of radius 4.2 cm surmounted by
a hemisphere of same radius.
Type 2, in a cone of radius 5.6 cm and height 4
cm surmounted by a hemisphere of same radius.
Gauri insisted to have ice-cream in first type while
her brother Dhruv decided to have the ice-cream
in second type. From the above information give
the answer of the following questions.
(i) While calculating the volume of the combined solids, we need:
a. add the volume of each solid
b. difference of the volume of both solids
c. to take same volume of each solid
d. none of the above
(ii) How much quantity of the ice-cream Gauri gets?
a. 266.11 cm3 b. 232.3 cm3 c. 273.11 cm3 d. 292.6 cm3
(iii) How much quantity of the ice-cream Dhruv gets?
a. 459.12 cm3 b. 499.32 cm3 c. 513.12 cm3 d. 519.23 cm3
C
B
A
O
P
Q
R
10.2cm
4.2 cm
4cm
5.6 cm
(iv) Out of the two, Gauri and Dhruv who got less quantity of ice-cream to
eat?
a. Gauri b. Dhriv c. Both got same quantity d. none of these
(v) How much more quantity of ice-cream get by Dhruv?
a. 233.21 cm3 b. 133.21 cm3 c. 193.31 cm3 d. 213.13 cm3
Answers
Given : An ice-cream seller sells his ice-creams in two ways:
Type 1, by Gauri : in a cone of radius 4.2 cm surmounted by a Hemisphere of same radius and total height 10.2cm
Type 2 by Dhruv, in a cone of radius 5.6 cm and height 4 cm surmounted by a hemisphere of same radius.
To Find : While calculating the volume of the combined solids, we need:
How much quantity of the ice-cream Gauri gets?
How much quantity of the ice-cream Dhruv gets?
Out of the two, Gauri and Dhruv who got less quantity of ice-cream to
eat?
How much more quantity of ice-cream get by Dhruv?
Solution:
While calculating the volume of the combined solids, we need to add the volume of each solid
Gauri ice-cream
cone of radius 4.2 cm , surmounted by a hemisphere of same radius. and height = 10.2cm
Hence cone height = 10.2 - 4.2 = 6cm
Volume of cone = (1/3)πr²h = (1/3)(22/7)(4.2)²6
= 110.88
Volume of Hemisphere = (2/3)πr³ = (2/3)(22/7)(4.2)³
= 155.232
Volume = 110.88 + 155.232 = 266.112 cm³
Gauri gets 266.11 cm³ ice cream
Dhruv ice-cream
cone of radius 5.6 cm and height 4 cm surmounted by a hemisphere of same radius.
Volume of cone = (1/3)πr²h = (1/3)(22/7)(5.6)²4
= 131.413
Volume of Hemisphere = (2/3)πr³ = (2/3)(22/7)(5.6)³
= 367.957
Volume = 131.413 + 367.957= 499.37 cm³
Dhruv gets 499.32 cm³ ice cream
Gauri gets lesser Quantity
more quantity of ice-cream get by Dhruv = 499.32 - 266.11
= 233.21 cm³
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