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.

Figure: First type: A Glass with hemispherical raised bottom.

Figure: 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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Isha got more quantity of juice than her father Suresh by 13.5π cm³.

Father Suresh got more quantity of juice than Isha by 20π cm³.

Father Suresh got more quantity of juice than Isha by 13.5π cm³.

Both Suresh and Isha got same quantity of juice.

answer is C.

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Detailed Solution

Given that, radii of both glasses, r = 3 cm and heights of both glasses, h = 10 cm.
Also, height of conical bottom = 1.5 cm.
Consider the first glass i.e., the glass with hemispherical bottom.
Question Image

We know that,
Volume of cylinder

= π r 2 h

Volume of hemisphere

= 23 π r 3

.
Here, the radius for both hemisphere and the cylinder are same.
Also, h = 10 cm and r = 3 cm.
The volume of juice in the first type of glass,
V1 = Volume of cylindrical glass – Volume of the hemisphere

∴ V 1 = π r 2 h − 23 π r 3 ∴ V 1 = π × 32 × 10 − 23 × π × 33 V 1 = (π × 9 × 10) − 23 × π × 27 V 1 = 90 π − 18 π V 1 = 72 π cm 3

Now, consider the second glass i.e., the glass with conical bottom.
Question Image

We know that,
Volume of cone

= 13 π r 2 h

Volume of cylinder

= π r 2 h

Here, height of cone = 1.5cm, height of cylinder = 10cm and radius = 3 cm.
So, the volume of juice in the first type of glass,
V2 = Volume of cylindrical glass – Volume of a cone

∴ V 2 = π r 2 h − 13 π r 2 h ′ ∴ V 2 = π × 32 × 10 − 13 × π × 32 × 1.5 V 2 = (π × 9 × 10) − 13 × π × 9 × 1.5 V 2 = 90 π − 4.5 π V 2 = 85.5 π cm 3

As we can observe, V1 < V2.
Hence, the father Suresh got more quantity of juice.
Now, let us find by how much volume Suresh gets more quantity of juice.