Question

How many balls, each of radius 3 cm can be made from a solid cone of lead of radius 9cm and height 20cm​

Answer 1

Step-by-step explanation:

Concept:

Volume remains unchanged of any solid when it is transformed into another shape.

Formula:

volume of cone

$= \frac{1}{3}\pi \: r {}^{2} h$

Volume of sphere

$= \frac{4}{3} \pi \: r {}^{3}$

Now decoding the question be like

$n \: \frac{4}{3} \pi \: 3 {}^{3} = \frac{1}{3} \pi \times 9 {}^{3} \times 20$

$n4 \times 3 {}^{3} = 9 {}^{3} \times 20 \\ n = 135$

Answer 2

Concept:

Volume remains unchanged of any solid when it is transformed into another shape.

Formula:

volume of cone

= \frac{1}{3}\pi \: r {}^{2} h =

3

1

πr

2

h

Volume of sphere

= \frac{4}{3} \pi \: r {}^{3} =

3

4

πr

3

Now decoding the question be like

n \: \frac{4}{3} \pi \: 3 {}^{3} = \frac{1}{3} \pi \times 9 {}^{3} \times 20n

3

4

π3

3

=

3

1

π×9

3

×20

\begin{gathered}n4 \times 3 {}^{3} = 9 {}^{3} \times 20 \\ n = 135\end{gathered}

n4×3

3

=9

3

×20

n=135