Advertisements
Advertisements
Question
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
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
Find the surface area of a sphere of diameter 21 cm.
`["Assume "pi=22/7]`
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
Find the radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
Find the surface area of a sphere of radius 5.6 cm .
A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
Find the total surface area of a hemisphere of radius 10 cm.
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
Mark the correct alternative in each of the following:
In a sphere the number of faces 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
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
The volume of a sphere is 905 1/7 cm3, find its diameter.
There is surface area and volume of a sphere equal, find the radius of sphere.
A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.
