Advertisements
Advertisements
Question
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.
Solution
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.
APPEARS IN
RELATED QUESTIONS
Find the amount of water displaced by a solid spherical ball of diameter 28 cm.
`["Assume "pi=22/7]`
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹ 4989.60 If the cost of white-washing is ₹ 20 per square meter, find the
- inside surface area of the dome,
- volume of the air inside the dome.
`["Assume "pi=22/7]`
Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the
- radius r' of the new sphere,
- ratio of S and S'.
The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?
A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?
A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1 .5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres?
A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.
A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.
