Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is (A) 4 cm (B) 3 cm (C) 2 cm (D) 6 cm

#Maths
#Exemplar Maths for Class 10
#NCERT
#Surface Areas and Volumes

#1.3
#9.2
#12.1
#12.2
#12.3
#12.4

1.0
1.0
1.0
1.0
2.0
2.0
2.0
2.0
3.0
3.0
3.0
4.0
4.0
4.0
4.0
4.0
5.0
5.0
5.0
6.0
6.0
6.0
6.0
6.0
6.0
7.0
7.0
7.0
7.0
8.0
8.0
8.0
8.0
9.0
9.0
9.0
9.0
10.0
10.0
11.0
11.0
11.0
11.0
12.0
12.0
12.0
12.0
12.0
13.0
13.0
13.0
13.0
13.0
14.0
14.0
14.0
15.0
15.0
15.0
16.0
16.0
16.0
17.0
17.0
18.0
18.0
18.0
19.0
19.0
20.0
31.0

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 6 cm

Answers (1)

Answer(C) 2 cm

Solution.

Diameter of metallic cylinder = 2 cm
$Radius$ $=\frac{2}{2}=1cm$
Height = 16cm
$Volume$ $=\pi r ^{2}h$
$=\pi \times 1 \times 1 \times 16= 16\pi$
We know that twelve solid spheres are made by melting of solid metallic cylinder
$\text{Volume of sphere}$ $=\frac{4}{3}\pi r^{3}$
$\text{Hence the volume of 12 spheres }$ $=16\pi$