# 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 - Mathematics

Match the Columns
Sum

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 withdiameter 14 m is dug upand the earth from diggingis evenly spread out to forma platform 44 m by 14 m.The height of the platformis ...........m. (q) 8 (c) A sphere of radius 6 cm ismelted and recast in theshape of a cylinder of radius4 cm. Then, the height of thecylinder is ......... cm. (r) 16 : 9 (d) The volumes of two spheresare in the ratio 64 : 27. Theratio 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

= 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 ofradius 8 cm is melted and thematerial is used to make solidright cones with height 4 cmand base radius of 8 cm.How many cones are formed? (q) 8 (b) A 20-m-deep well withdiameter 14 m is dug upand the earth from diggingis evenly spread out to forma platform 44 m by 14 m.The height of the platformis ...........m. (s) 5 (c) A sphere of radius 6 cm ismelted and recast in theshape of a cylinder of radius4 cm. Then, the height of thecylinder is ......... cm. (p) 18 (d) The volumes of two spheresare in the ratio 64 : 27. Theratio of their surface areas is ....... . (r) 16 : 9
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Multiple Choice Questions | Q 74 | Page 925