Question

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are trans- ferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is

Answer 1

Answer:

• The hemispherical bowl contains a beverage.
• The content of the bowl is transferred to a cylindrical vessel.
• The radius of the cylindrical vessel is 50% more than its height.
• The diameter of a cylindrical vessel and the hemispherical bowl is same.

We need to find the volume of the beverage i. the cylindrical vessel.

As, Given, the diameter of both the cylindrical vessel and the hemispherical bowl is same.

Hence, the radius of the cylindrical vessel and the hemispherical bowl can be taken as r.

So, Radius = r.

Now, given that the radius of the cylindrical vessel is 50% more than its height.

Hence, r = h + ½h

➜ r = 3/2 h

So, h = 2/3 r

The formula to find the volume of cylinder = πr²h.

The formula to find the volume of a hemisphere = 2/3 πr³

Now, substituting the values in the first formula.

➜ π * r² * 2/3 r

➜ 2/3 π r³

Now, here we observed that the volume of both the vessels are the same i.e. 2/3 π r³.

Hence, the Volume of the beverage = 2/3 π r³.

The Volume of beverage in the cylindrical vessel is to be found out here.

Hence, (Volume of beverage in hemispherical bowl÷Volume of beverage in cylindrical vessel)*100%.

So, (2/3πr³)/(2/3πr³) * 100%

➜ 100% of the beverage is in the cylindrical vessel.

Answer 2

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QUESTION -

A hemispherical bowl is filled to the brim with a beverage.

The contents of the bowl are trans- ferred into a cylindrical vessel whose radius is 50% more than its height.

If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is ..........

SOLUTION -

From the above Question, we can gather the following information......

A hemispherical bowl is filled to the brim with a beverage.

The contents of the bowl are trans- ferred into a cylindrical vessel whose radius is 50% more than its height.

The diameter is same for both the bowl and the cylinder.

Let the radius of the required Cylinder be r.

Now,

150% H = r

=> ( 3 / 2 ) H = r

=> H = ( 2 / 3 ) r.

$\tt{\orange{\boxed{\boxed{ H = \dfrac{2}{3} r }}}}$

Now, we know that -

Volume of any right circular cylinder is π r ^ 2 h.

So,

Volume = π × r ^ 2 × r × ( 2 / 3 ) = ( 2 / 3 ) π r ^ 3.

We also know that :

Volume of a hemisphere is ( 2 / 3 ) π r ^ 3.

Hence we find that for a given radius , the volume of both the cylinder and the hemisphere is equal.

So,

The volume of the beverage in the cylindrical vessel is equal to the volume of the beverage in the cylinder.

ANSWER ;

The volume of the beverage in the cylindrical vessel is equal to the volume of the beverage in the cylinder.