Question

the ratio of radio of two spheres is 2:3, find the ratio of their surface area and volumes​

Answer 1

Answer:

ratio of surface areas of spheres= 4:9

ratio of volumes of spheres = 8: 27

Step-by-step explanation:

ratio of radii of two spherea is 2:3, therefore,

radius of one sphere = 2

radius of another sphere = 3

now, surface area of sphere = 4πr², therefore,

ratio of surface areas of two spheres,

4π(2²):4π(3²)

2²: 3²

4 : 9

now, volume of sphere = 4/3πr³, therefore,

ratio of volumes of two spheres,

4/3π(2³) : 4/3π(3³)

2³: 3³

8 : 27

Answer 2

Given Question :-

• The ratio of radius of two spheres is 2:3, find the ratio of their surface area and volumes.

Answer

Given :-

• Two spheres, such that ratio of their radius is 2 : 3

To Find :-

• Ratio of their Surface Areas.

• Ratio of their Volumes.

Formula Used :-

${ \boxed{\bf{Surface area_{(sphere)} = 4\pi \: {r}^{2} }}}$

$\boxed{ \bf{Volume_{(sphere)} = \dfrac{4}{3} \pi \: {r}^{3} }}$

Solution :-

Given that

• Two spheres, such that ratio of their radius is 2 : 3.

• Let radius of first sphere be 2r

and

• Let radius of second sphere be 3r

Now,

Ratio of the surface area of two spheres are

$\sf \: \dfrac{Surface area_{(sphere \: 1)}}{Surface area_{(sphere \: 2)}} = \dfrac{4\pi \: {(2r)}^{2}}{4\pi \: {(3r)}^{2}} = \dfrac{4}{9}$

Hence,

$\sf \: Surface area_{(sphere \: 1)} : Surface area_{(sphere \: 2)} = 4 : 9$

Now,

Ratio of the Volume of two spheres are

$\sf \: \dfrac{Volume_{(sphere \: 1)}}{Volume_{(sphere \: 2)}} = \dfrac{\dfrac{4}{3} \pi \: {(2r)}^{3}}{\dfrac{4}{3} \pi \: {(3r)}^{3}} = \dfrac{8}{27}$

$\sf \: Volume_{(sphere \: 1)} : Volume_{(sphere \: 2)} = 8 : 27$

More information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²