two solid spheres made of the same metal have weights 5920g and 740g respectively. determine the radius of the larger sphere ,if the diameter of small one is 5cm.
Answers
Answer:
Step-by-step explanation:
Secondary SchoolMath 8+4 pts
Two solid spheres made of same metal have masses 5920g and 740g. determine the radius of the largest sphere if the diameter of the smallest sphere is 5cm. urgent....
Solution:-
Given :- Weight of the heavier sphere = 5920 g and weight of the lighter sphere = 740 g, and diameter of lighter sphere = 5 cm or radius = 2.5 cm
Let the volume of the heavier sphere be 'V1' and the volume of the lighter sphere be 'V2'. Radius of the heavier sphere be 'r1' because the diameter of the lighter sphere is given so the radius is 2.5 cm.
Weight of an object = density × volume of that object
So,
(Weight of the heavier sphere/weight of the lighter sphere) = (Density × V1/density × V2)
As both the spheres are made up of same metal, therefore, the ratio of their weights will be equal to the ratio of their volumes.
(weight of the heavier sphere/weight of the lighter sphere) = (V1/V2)
⇒ (5920/740) = (4/3πr₁³)/(4/3πr³)
⇒ (5920/740) = (4/3 × 22/7× r₁³)/(4/3 × 22/7 × 2.5 × 2.5 × 2.5)
⇒ 8 = r₁³ × 1/2.5 × 1/2.5 × 1/2.5
⇒ 8 = r₁³ × 1/15.625
⇒ r₁³ = 8 × 15.625
⇒ r₁³ = 125
⇒ r₁ = 5 cm
So, the radius of the heavier sphere is 5 cm.
Answer.
Answer:heavier sphere=5cm
Step-by-step explanation: