Two solid spheres made of the same metal have weight `5920` `g` and `740` `g`, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is `5` `cm`.

Explanation

Given, weight of one solid sphere, `m_(1) = 5920 g`
and wieght of another solid sphere, `m_(2) = 740 g`
Diameter of the smaller sphere = 5 cm
`therefore` Radius of the smaller sphere, `r_(2) = (5)/(2), m_(2)= 740 g`
We know that, `"Density " =("Mass (M)")/("Volume(D)")`
`rArr " ""Volume", V = (M)/(D)`
`rArr " "V_(1) = (5920)/(D)cm^(3)" "....(i)`
and " "`V_(2) = (740)/(D) cm^(3)" ".....(ii)`
On dividing Eq. (i) by Eq. (ii), we get
`(V_(1))/(V_(2)) =((5920)/(D))/((740)/(D))`
`because" ""Volume of a sphere" = (4)/(3)pir^(3)`
`((4)/(3) pir_(1)^(3))/((4)/(3) pir_(2)^(3)) =(5920)/(740) rArr ((r_(1))/(r_(2)))^(3) = (592)/(74)`
`rArr" "((r_(1))/(5//2))^(3) = (592)/(74)" "[because r_(2) =(5)/(3)cm]`
`rArr (r_(1)^(3))/((125)/(8)) = (592)/(74)rArr (8r_(1)^(3))/(125)= (592)/(74)`
`rArr " "r_(1)^(3) = (592)/(74) xx (125)/(8) = (74000)/(592) = 125`
`therefore" "r_(1) = 5 cm` " "[taking positive value of the cube road]
Hence, the radius of large sphere is 5 cm.