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प्रश्न
Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.
उत्तर
Given, Weight of one solid sphere, m1 = 5920 g
And weight of another solid sphere, m2 = 740 g
Diameter of the smaller sphere = 5 cm
∴ Radius of the smaller sphere, r2 = `5/2`, m2 = 740 g
We know that, Density = `("Mass" (M))/("Volume" (D))`
⇒ Volume, `V = M/D`
⇒ `V_1 = 5920/D cm^3` ...(i)
And `V_2 = 740/D cm^3` ...(ii)
On dividing eqution (i) by equation (ii), we get
`V_1/V_2 = (5920/D)/(740/D)`
∵ Volume of a sphere = `4/3 pir^3`
`(4/3 pir_1^3)/(4/3 pir_2^3) = 5920/740`
⇒ `(r_1/r_2)^3 = 592/74`
⇒ `(r_1/(5/2))^3 = 592/74` ...`[∵ r_2 = 5/2 cm]`
⇒ `r_1^3/(125/8) = 592/74`
⇒ `(8r_1^3)/125 = 592/74`
⇒ `r_1^3 = 592/74 xx 125/8`
= `74000/592`
= 125
∴ r1 = 5 cm ...[Taking positive value of the cube root]
Hence, the radius of larger sphere is 5 cm.
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