Question

Take a hemisphere and a cylinder with an equal base and height. fill the hemisphere with water than pour the water into the cylinder, how far up the cylinder will the water reach?

Answer 1

Answer:

2/3rd

Step-by-step explanation:

2/3πr³=πr²h

2/3πr³=πr³ (r=h, given in the question)

2/3=1

so, if we take hemisphere and a cylinder with an equal base and height, volume of hemisphere will be 2/3rd of the volume of cylinder. so the water fills 2/3rd portion of cylinder

Answer 2

The cylinder will fill up to 2/3rd part.

Given:

• Take a hemisphere and a cylinder with an equal base and height.
• Fill the hemisphere with water then pour the water into the cylinder

To find:

• How far up the cylinder will the water reach?

Solution:

Formula to be used:

Volume of hemisphere: $\bf V_H = \frac{2}{3} \pi \: {r}^{3}$

Volume of cylinder: $\bf V_C = \pi {r}^{2} h$

Step 1:

Write the given terms.

ATQ,

Radius of Base (r)= Height (h)

Radius of hemisphere and cylinder is same.

Step 2:

Find the water level of cylinder.

Volume of Hemisphere

$V_H = \frac{2}{3} \pi {r}^{3} ...eq1$

Volume of cylinder

$V_C = \pi {r}^{2} r$

As h=r

$V_C = \pi {r}^{3}...eq2$

Equate both eqs 1 and eq2.

$V_H = V_C$

$\frac{2}{3} \pi {r}^{3} = \pi {r}^{3}$

$\text{\bf Water level}\bf = \frac{2}{3}\text{\bf Volume of cylinder}$

Thus,

The cylinder will fill up to 2/3rd part.

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