The volume of two sphere are
640 cm3
and 240 cm3 ? Find the ratio of their
diameters?
Answers
Given :
- Volume of two spheres :-
- Volume of the first sphere = 640 cm³
- Volume of the second sphere = 240 cm³
To find :
- Ratio of their diameters
Concept :
To calculate the radius of their diameters, firstly calculate the radius of the two spheres. Multiply the radius by 2, the resultant value will be the diameter of the sphere. Now, after dividinh both the diameters the resultant value which we'll get will be the ratio of the diameter of both the spheres.
Formula of volume of sphere :-
- Volume of sphere = 4/3 πr³
where,
- Take π = 22/7
- r = radius
Formula to calculate diameter :-
- Diameter = 2 × Radius
Solution :
Radius of the first sphere :-
→ Volume of the sphere = 4/3 πr³
Substituting the given values,
→ 640 = 4/3 × 22/7 × r³
→ 640 = 88/21 × r³
→ Transposing 88/21 to the left hand side. While transpoing the denominator will change into numerator and the numerator will change into denominator.
→ 640 × 21/88 = r³
→ 320 × 21/44 = r³
→ 160 × 21/22 = r³
→ 80 × 21/11 = r³
→ 1680/11 = r³
→ 152.73 = r³
→ Taking cube root on both the sides.
→ 5.35 = r
- Radius of the first sphere = 5.35 cm
Diameter of the first sphere :-
→ Diameter = 2 × Radius
Substitute the given value,
→ Diameter = 2 × 5.35
→ Diameter = 10.7
- Diameter of the first sphere = 10.7 cm
Radius of the second sphere :-
→ Volume of the second sphere = 4/3 πr³
Substituting the given values,
→ 240 = 4/3 × 22/7 × r³
→ 240 = 88/21 = r³
→ Transpoing 88/21 to the other side.
→ 240 × 21/88 = r³
→ 120 × 21/44 = r³
→ 60 × 21/22 = r³
→ 30 × 21/11 = r³
→ 57.27 = r³
→ Taking cube root on both the sides.
→ 3.85 = r
- Radius of the second sphere = 3.85 cm
Diameter of the second sphere :-
→ Diameter = 2 × Radius
Substitute the given value,
→ Diameter = 2 × 3.85
→ Diameter = 7.7
- Diameter of the second sphere = 7.7 cm
Ratio of the diameter of the two spheres :-
→ Ratio = 10.7 ÷ 7.7
→ Ratio = 1.39
Therefore,
- Ratio of their diameters = 1.39 cm