Question

The volume of a solid hemisphere is 29106.Another hemisphere

Answer 1

Answer:

Step-by-step explanation:

Hemisphere:

Hemisphere is the exact half of a sphere. The volume of a solid hemisphere =  

1

2

(

volume of sphere

)

. The volume of a solid hemisphere is  

2

3

π

r

3

c

u

.

u

n

i

t

s

.

Answer and Explanation:

Solution

:

Let r be the radius of the hemisphere

.

Given that, volume of the hemisphere

=

29106

c

m

3

Now, volume of new hemisphere

=

2

3

(

Volume of original sphere

)

=

2

3

×

29106

The volume of new hemisphere

=

19404

c

m

3

2

3

π

r

3

=

19404

r

3

=

19404

×

3

×

7

2

×

22

=

9261

r

=

3

√

926

=

21

c

m

r

=

21

c

m

Therefore, the radius of the new hemisphere

r

=

21

c

m

Answer 2

The complete question:

The volume of a solid hemisphere is 29106 $cm^3$. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

Given:

The volume of a solid hemisphere = 29106 $cm^3$

Let the radius of the new hemisphere = r

We have to find, the value of the radius of the new hemisphere (r).

Solution:

According to question,

The volume of the new hemisphere = $\dfrac{2}{3}$(The volume of original sphere)

= $\dfrac{2}{3}$ × 29106 $cm^3$

= 19404  $cm^3$

∴ The volume of the new hemisphere = 19404  $cm^3$

We know that,

The volume of the hemisphere = $\dfrac{2}{3}\pi r^3$

∴ $\dfrac{2}{3}\times \dfrac{22}{7} r^3$ = 19404

⇒ $r^{3}$ = 9261

⇒ $r^{3}$ = $21^{3}$

⇒ r = 21 cm

Thus, the radius of the new hemisphere (r) is "21 cm".