Question

A glass in the form of a right circular cylinder is half full of water. Its base diameter is 6 cm and height is 8 cm. The volume of water is
9π cm³
18π cm³
36 cm³
36π cm³


explain how you did it-

Answer 1

Given:

• A glass in the form of a right circular cylinder .

• Base diameter = 6 cm

• Height = 8 cm

To calculate:

• Volume of water

Clarification:

Clearly, here it is stated that glass is half full of water.So, the volume of water will be half of the volume of the glass.

At first, we'll calculate the volume of the glass through the given information. Then, we'll divide it by 2 in order to find the volume of water.

Solution:

According to the question,

→ $\sf { {Volume}_{Water}= \dfrac{Volume_{Glass} }{2} }$

[ As it is filled half of the glass.]

Let's calculate the volume of the cylindrical glass first.

→ Volume of the cylindrical glass = πr²h

We aren't given the value of radius. So, let's calculate it. We know that,

⠀⠀⠀⠀⠀⠀⠀⇒ Diameter = 2 × Radius

⠀⠀⠀⠀⠀⠀⠀⇒ Radius = $\sf { \dfrac{D}{2} }$

⠀⠀⠀⠀⠀⠀⠀⇒ Radius = $\sf{\dfrac{6}{2}}$cm

⠀⠀⠀⠀⠀⠀⠀⇒ Radius = 3 cm

Now,

→ Volume of the cylindrical glass = [ π × (3)² × 8 ] cm³

→ Volume of the cylindrical glass = [ π × 9 × 8 ] cm³

→ Volume of the cylindrical glass = [ π × 72 ] cm³

→ Volume of the cylindrical glass = 72π cm³

So,

→ $\sf { {Volume}_{Water}= \dfrac{Volume_{Glass} }{2} }$

→ $\sf { {Volume}_{Water}=\dfrac{72 \pi }{2} {cm}^{3}}$

→ Volume of water = 36π cm³

Therefore, the volume of water is 36π cm³.

Option D is correct.

Answer 2

Volume of Glass = 2(Volume of Water)

⇒ V = 2v

⇒ v = V/2

Now, volume of a right circular cylinder = πr²h

∴ v = (πr²h)/2

⇒ v = (π · 3² · 8)/2

⇒ v = 9π · 4

⇒ v = 36π.

∴ Volume of water inside the container was of 36π cm³.

(Option D)