A MATALLIC SPHERE OF RADIUS 10.5 cm IS MELTED AND THEN RECAST INTO SMALLER CONES EACH OF RADIUS 3.5 cm AND HEIGHT 3 cm HOW MANY CONES ARE OBTAINED?
Answers
Step-by-step explanation:
Given,
Radius of metallic sphere R=10.5 cm
Radius of circular base of smaller cone r=3.5 cm
Hight of cone h=3 cm
Volume of metallic sphere V=
3
4
πR
3
=
3
4
×
7
22
×(10.5)
3
cm
3
=
3
4
×
7
22
×1157.625 cm
3
=
21
88
×1157.625 cm
3
=88×55.125 cm
3
Volume of metallic sphere V=4851 cm
3
Volume of one cone v=
3
1
π r
2
h
=
3
1
×
7
22
×(3.5)
2
×3 cm
3
=
7
22
×12.25 cm
3
Volume of one cone=38.5 cm
3
Number of cones formed n=
Volume of one cone (v)
Volume of sphere(V)
n=
38.5 cm
3
4851 cm
3
n=126
Hence the solid sphere can be melted in 126 smaller cones .
Answer:
Given,
Radius of metallic sphere R=10.5 cm
Radius of circular base of smaller cone r=3.5 cm
Hight of cone h=3 cm
Volume of metallic sphere V = 4/3 πR³
4/3×22/7×(10.5)³
Volume of metallic sphere V=4851 cm³
Volume of one cone v = 1/3πR²h
1/3×22/7×(3.5)²×3 cm³
Volume of one cone=38.5 cm³
Number of cones formed n=
Volume of sphere(V)/Volume of cone(V)
4851/38.5
n=126
Hence the solid sphere can be melted in 126 smaller cones .