Question 26 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Nov. 1, 2019 by Teachoo

Isha is 10 years old girl. On the result day, Isha and her father Suresh were very happy as she got first position in the class. While coming back to their home, Isha asked for a treat from her father as a reward for her success. They went to a juice shop and asked for two glasses of juice.

Aisha, a juice seller, was serving juice to her customers in two types of glasses. Both the glasses had inner radius 3cm. The height of both the glasses was 10cm.

First type: A Glass with hemispherical raised bottom.

Second type: A glass with conical raised bottom of height 1.5 cm.

Isha insisted to have the juice in first type of glass and her father decided to have the juice in second type of glass. Out of the two, Isha or her father Suresh, who got more quantity of juice to drink and by how much?

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Question 26 Isha is 10 years old girl. On the result day, Isha and her father Suresh were very happy as she got first position in the class. While coming back to their home, Isha asked for a treat from her father as a reward for her success. They went to a juice shop and asked for two glasses of juice. Aisha, a juice seller, was serving juice to her customers in two types of glasses. Both the glasses had inner radius 3cm. The height of both the glasses was 10cm.
First type: A Glass with hemispherical raised bottom.
Second type: A glass with conical raised bottom of height 1.5 cm. Isha insisted to have the juice in first type of glass and her father decided to have the juice in second type of glass. Out of the two, Isha or her father Suresh, who got more quantity of juice to drink and by how much?
Here,
We need to find Volume of both glasses and find which has more volume
Type A
Volume of glass
= Volume of cylinder of h = 10 cm & r = 3 cm
– Volume of Hemisphere of r = 3 cm
= πr2h – 2/3 πr3
= π × 32 × 10 – 2/3 × π × 33
= π × 9 × 10 – 2 × π × 32
= 90π – 18π
= 72π
Type B
Volume of glass
= Volume of cylinder of h = 10 cm & r = 3 cm
– Volume of Cone with height = hc = 1.5 cm & r = 3 cm
= πr2h – 1/3 πr2hCone
= π × 32 × 10 – 1/3 × π × 32 × 1.5
= π × 9 × 10 – π × 3 × 1.5
= 90π – 4.5π
= 85.5π
Since Volume of Type B Glass is bigger
∴ Suresh got more juice
Difference in quantity = 85.5π – 72π
= 13.5π

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.