Advertisements
Advertisements
प्रश्न
Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is ______.
विकल्प
3 : 4
4 : 3
9 : 16
16 : 9
उत्तर
Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is 16 : 9.
Explanation:
Let the radii of the two spheres are r1 and r2, respectively.
∴ Volume of the sphere of radius,
r1 = V1 = `4/3 pi"r"_1^3` ...(i) [∵ Volume of sphere = `4/3pi` (radius)3]
And volume of the sphere of radius,
r2 = V2 = `4/3 pi"r"_2^3` ...(ii)
Given, ratio of volumes = V1 : V2 = 64 : 27
⇒ `(4/3 pi"r"_1^3)/(4/3 pi"r"_2^3) = 64/27` ...[Using equations (i) and (ii)]
⇒ `("r"_1^3)/("r"_2^3) = 64/27`
⇒ `"r"_1/"r"_2 = 4/3` ...(iii)
Now, ratio of surface area = `(4 pi"r"_1^2)/(4 pi"r"_2^2)` ...[∵ Surface area of a sphere = 4π (radius)2]
= `"r"_1^2/"r"_2^2`
= `("r"_1/"r"_2)^2`
= `(4/3)^2` ...[Using equation (iii)]
= 16 : 9
Hence, the required ratio of their surface area is 16 : 9.
APPEARS IN
संबंधित प्रश्न
A wall 24 m , 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm \[\times\] 16 cm \[\times\] 10 cm . If the mortar occupies \[\frac{1}{10}th\] of the volume of the wall, then find the number of bricks used in constructing the wall.
What is the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
The curved surface area of a cylinder is 264 m2 and its volume is 924 m3. The ratio of its diameter to its height is
Water is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 60 m long and 22 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of ₹25 per metre.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hr, then in how much time will the tank be filled completely?
The dimensions of a metallic cuboid are 44 cm × 42 cm × 21 cm. it is molten and recast into a sphere. Find the surface area of the sphere.
In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4⋅2 cm. Find
(a) the total surface area of the block.
(b) the volume of the block formed. `("Take" pi = 22/7)`
______ surface area of room = area of 4 walls.
The radius of a metal sphere is 3 cm. The sphere is melted and made into a long wire of uniform circular cross-section, whose length is 36 cm. To calculate the radius of wire, complete the following activity.
Radius of the sphere = `square`
Length of the wire = `square`
Let the radius of the wire by r cm.
Now, Volume of the wire = Volume of the `square`
`square` = `square`
r2 × `square` = `square` × `square`
r2 × `square` = `square`
r = `square`
Hence, the radius of the wire is `square` cm.
