(31) A closed wooden box with external dimensions  80 cm × 60 cm × 40 cm  is made of  5 cm thick wood. If  1 cm³ of  wood weighs 10 gms, find the weight  of  the empty box.

Soln. Volume of  wood  =  [( 80 × 60 × 40 ) – ( 70 × 50 × 30 )]  =  87000 cm³.

Weight of  the empty box  =    =  870  gm.  =  0.870  kg.

(32) Find the volume, curved surface area and the total surface area of  a cylinder of  length  50 cm with diameter of  the base 14 cm.

Soln. Here   r  = 7 cm   and   h  = 50  cm.

∴  Volume of  the cylinder  = πr²h  =   × 7 × 7 × 50  =  7700 cm³.

Curved surface area of  the cylinder  =  2πr h  =  2 × × 7 × 50  =  2200 cm²

Total surface area  =  2πr ( h + r )   =    2 ×  × 7 × ( 50 + 7 )  =  2508 cm².

(33) A powder tin has a square base with side 7 cm and height 10 cm. Another tin has a circular base with diameter 7 cm and height 10 cm. Find the difference in their capacities.

Soln. Volume of  rectangular  tin  =  ( l × b × h )  =  ( 7 × 7 × 10 )  =  490 cm³.

Volume of  cylindrical  tin  = π r²h  =    =  385 cm³.

∴ Difference in their capacities  =  ( 490 – 385 )  =  105  cm³.

(34) A well with 42 m inside diameter is dug 7 m deep. The earth taken out of  it has been evenly spread all around it to a width of  21 m to form an embankment. Find the height of  the embankment.

Soln.

Area of  embankment

=   π ( R² – r² )

=    × [ ( 28 ) ² – ( 7 ) ² ]

=  × 21 × 35   m³

Now,  Volume of  embankment  =  volume of  earth dug out

∴   Area of  embankment  ×  Height  =   × 21 × 21 × 7

∴  × 21 × 35  ×  h  =  × 21 × 21 × 7

∴    h  =  4.2  m

(35) How many iron rods, each of  length 7 m and diameter 2 cm can be made out of  0.44 cubic meter of  iron ?

Soln.

Number of  rods =   

=   

=   

=     200

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