Advertisements
Advertisements
Question
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
Advertisements
Solution
Let r be the radius of the sphere.
Surface area = 4πr2 and volume = `4/3pir^3`
According to the condition:
`4pir^2 = 4/3pir^3`
`=> r^3/r^2 = 4pi xx 3/(4pi)`
`=>` r = 3 cm
Diameter of sphere = 2 × 3 cm = 6 cm
RELATED QUESTIONS
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["Assume "pi=22/7]`
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
The total surface area of a hemisphere of radius r is
If the surface area of a sphere is 144π m2, then its volume (in m3) is
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast. `("Take" pi =22/7)`
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
