(21) A room is half as long again as it is broad. The cost of  carpeting the room at Rs. 20 per m² is Rs. 3000 and the cost of  white-washing the 4 walls at Rs. 6 per m² is Rs.1200. Find the dimensions of  the room.

Soln. Let breadth  =  x, length  =    and  height  =  y metres.

Now, area of  the carpet

= 

= 

=   150  m²

Again,

area of  four walls

= 

∴   2 ( l + b ) ×h  = 

∴ 2 ( 15 + 10 ) ×h  =  200

∴ h  =  4

∴ height  =  4 m

Now,

Area of  a room  = Area of  the Carpet

∴   x ×  =   150

∴   x    =   10

∴   length  =  15 m  &  breadth  =  10 m

(22) A rectangular grassy plot is 100 m by 55 m.  It has a gravel path 2.5 m wide all round it on the inside. Find the area of  the path.

Soln. Area of  the path

=   Area of  big rectangle  –  Area of  small rectangle

=   ( 100  ×  55 )  –  ( 95  × 50 )

=   5500  –  4750

=   750   m²

(23) Find the volume, surface area and the diagonal of  a cuboid, 10 m long, 8 m broad and 5 m high.

Soln. Volume  =   l b h   =   10 × 8 × 5   m³  =  400 m³.

Surface Area =    2 ( lb +  bh + lh )

=    2 [ ( 10×8 ) + ( 8 × 5 ) + ( 10 × 5 ) ]   =  340   m²

Diagonal   = 

= 

= 

=   m

(24) Find the volume, surface area and the diagonal of  a cube, each of  whole sides measures 5 cm.

Soln. Volume   =   l³  =   5 × 5 × 5   =  125  cm³.

Surface area   =   6 l²  =    6 × 5 × 5   =  150 cm².

Diagonal  =  l  =   × 5  =  1.732 × 5  =  8.66 cm.

(25) The surface area of  a cube is 600 cm². Find its volume.

Soln. 6 l²   =  600   ⇒  l²  =  100    ⇒   l  =  10 cm.

Volume  =  l³  =   10³  =  1000 cm³.

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