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 20mdeep 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 
Solution
(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
= πr^{2}h
`= 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
= πr^{2}h
= 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 20mdeep 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
