Question

Match the following columns:

Column I	Column II
(a) A solid metallic sphere of radius 8 cm is melted and the material is used to make solid right cones with height 4 cm and base radius of 8 cm. How many cones are formed?	(p) 18
(b) A 20-m-deep well with diameter 14 m is dug up and the earth from digging is evenly spread out to form a platform 44 m by 14 m. The height of the platform is ...........m.	(q) 8
(c) A sphere of radius 6 cm is melted and recast in the shape of a cylinder of radius 4 cm. Then, the height of the cylinder is ......... cm.	(r) 16 : 9
(d) The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is ....... .	(s) 5

Answer 1

(a)

Volume of the surface`= 4/3 pi"r"^3`

`=(4/3pixx(8)^3) "cm"^3`

Volume of each cone`= 1/3 pi"r"^2h`

`= 1/3 pixx(8)^2xx4 "cm"^3` 

`"Number of cones formed"="Volume of the sphere"/"Volume of each cone"` 

`=(4pixx8xx8xx8xx3)/(3xxpixx8xx8xx4)`

= 8

Hence, (a) ⇒ (q)

(b)
Volume of the earth dug out = Volume of the cylinder

= πr²h

`= 22/7xx7xx7xx20 = 44xx14xx"h"`

Let the height of the platform be h.
Then, volume of the platform = volume of the cuboid

`= (44 xx 14 xx "h") "m"^3` 

Therefore,

`22/7xx7xx7xx20= 44xx14xx"h"`

`=> 3080 = 616xx"h"`

`=> "h" = 3080/616`

⇒ h = 5 m

Hence, (b) ⇒ (s)

(c)

Volume of the sphere`= 4/3pi"r"^3`

`= 4/3 pixx6xx6xx6`

Let h be the height of the cylinder.

Then, volume of the cylinder

= πr²h

= π × 4 × 4 × h

Therefore,

`4/3pixx6xx6xx6 = pixx4xx4xx"h"` 

`=> 4/3xx6xx6xx6xx = 4xx4xxh`

`=> 228=16xx"h"`

`=>"h" = 228 /16`

⇒ h = 18 cm

Frence , (c) ⇒ ( p )

(d) 

Let the radii of the spheres be R and r respectively. 

Then , ratio of their Volumes `= (4/3pi"R"^3)/(4/3pi"r"^3)`

Therefore, 

`(4/3pi"R"^3)/(4/3pi"r"^3)= 64/27`

`=> "R"^3/"r"^3 = 64/27`

`=>("R"/"r") = (4/3)^3`

`= "R"/r = 4/3`

Hence, the ratio of their surface areas `= (4pi"R"^2)/(4pi"r"^2)`

`="R"^2/"r"^2`

`=("R"/"r")^2`

`=(4/3)^2`

`= 16/9`

= 16 : 9

Hence, (d) ⇒ (r)

Column I	Column II
(a) A solid metallic sphere of radius 8 cm is melted and the material is used to make solid right cones with height 4 cm and base radius of 8 cm. How many cones are formed?	(q) 8
(b) A 20-m-deep well with diameter 14 m is dug up and the earth from digging is evenly spread out to form a platform 44 m by 14 m. The height of the platform is ...........m.	(s) 5
(c) A sphere of radius 6 cm is melted and recast in the shape of a cylinder of radius 4 cm. Then, the height of the cylinder is ......... cm.	(p) 18
(d) The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is ....... .	(r) 16 : 9