Question

Height of a solid metal cone is 12 centimetres. Its radius is 9 centimetres.

a) Find the volume of the cone.

b) How many spheres of radius 1 centimetre can be made by melting and recasting the cone?
Plz answer with steps​

Answer 1

Answer:

Step-by-step explanation:

Volume of cone= 3/1 πr 2 h

Here, for cone r=12,h=24

= 3/1 ×π×122 ×24= 31 ×π×144×24

=1152πcm 2

Volume of balls(sphere) = 3/4

​

πr

3

Here, for ball r= 2/6

​ =3 /34 π×3 3

=36π

No. of balls= 36π1152π

​ =32

Thus 32 balls will be formed.

Answer 2

Answer:

(a) Volume of cone is 1018.28 $cm^{3}$

(b) 243 spheres of radius 1 centimetre can be made by melting and recasting the cone.

Step-by-step explanation:

Let 'h' be the height and 'r' be the radius of the cone.

(a) Volume of cone = $\frac{1}{3} \times \pi \times r^{2} \times h$

= $\frac{1}{3} \times \frac{22}{7} \times 9^{2} \times12$

=$1018.28\ cm^{3}$

(b) Let 'n' number of spheres can be made by melting and recasting the cone.

According to the given data,

Volume of cone = 'n' x Volume of each sphere

$1018.28=\frac{4}{3} \times \pi \times r^{3}$

$1018.28=n\times\frac{4}{3} \times\frac{22}{7} \times 1^{3}$

$\therefore$ $n=243$

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