Advertisements
Advertisements
Question
The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
Options
1 : 2
2 : 3
9 : 16
16 : 9
Solution
Ist sphere
`V_1 = 4/3 pir_1^2`…… (i)
IInd sphere
`V_2 = 4/3 pir_2^3`…… (ii)
Divide (i) by (ii) we get,
`V_1/V_2 = (4/3pi r_1^3)/(4/3pi r_2^3)`
`64/27 = (r_1/r_2)^3`
`r_1/r_2 = sqrt(64/27)`
`r_1/r_2 = 4/3`
Now, the ratio of their C.S.A
`S_1/S_2 = (4pir_1^2)/(4pir_2^2)= (r_1/r_2)^2`
`S_1/S_2 = (4/3)^2 = 16/9`
Hence, `S_1 :S_2 = 16 :9`
APPEARS IN
RELATED QUESTIONS
A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.
The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is
The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is ______.
The length of the longest pole that can be kept in a room (12 m × 9 m ×8 m) is
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3 . the radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it.
The surface area of a sphere is 616 cm2. Its radius is ______.
Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.
A bicycle wheel makes 500 revolutions in moving 1 km. Find the diameter of the wheel.
The surface area of a sphere is 616 sq cm. Find its radius tan β = `3/4`
