Advertisements
Advertisements
Question
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
Advertisements
Solution
Volume of first sphere = 27 × volume of second sphere
Let radius of first sphere = r1
And radius of second sphere = r2
Therefore, volume of first sphere = `4/3pir_1^3`
And volume of second sphere = `4/3pir_2^3`
i. Now, according to the question
= `4/3pir_1^3`
= `27 xx 4/3pir_2^3`
`r_1^3 = 27r_2^3 = (3r_2)^3`
`=>` r1 = 3r2
`=> r_1/r_2 = 3/1`
∴ r1 : r2 = 3 : 1
ii. Surface area of first sphere = `4pir_1^2`
And surface area of second sphere = `4pir_2^2`
Ratio in surface area = `(4pir_1^2)/(4pir_2^2)`
= `r_1^2/r_2^2`
= `3^2/1^2`
= `9/1`
= 9 : 1
APPEARS IN
RELATED QUESTIONS
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 radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
Find the surface area of a sphere of radius 10.5 cm.
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 Rs. 4 per 100 `cm^2`
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
The volume of a sphere is 905 1/7 cm3, find its diameter.
