Question

1]A contractor agrees to dig a basement 8mx6mx3m.How many cubic meters of earth will be taken out?
2]A rectangular sheet of paper of dimensions 25cmx14cm is revolved along its width to form a cylinder.Find the volume of the cylinder so formed.
3]A HOLLOW CYLINDRICAL PIPE IS 1.4m long.Its outer and inner diameters are cm and cm respectively.Find the volume of the metal used in making pipe.

Answer 1

1. The earth to be taken out = volume of the basement = 8×6×3 = 144m³

2. length of sheet = 25cm
width of sheet = 14 cm
if it is revolved along its width to form a cylinder,
height = length of sheet = 25cm
perimeter = width of sheet = 14 cm

$2 \pi r = 14\\2* \frac{22}{7}*r=14\\r= \frac{14*7}{2*22} =2.23\ cm$

$volume= \pi r^2h= \frac{22}{7}*2.23^2*25=390.73\ cm^3$

3.length = 1.4 m = 140cm
inner diameter($d_i$)=10cm
inner radius($r_i$) = 10/2 = 5 cm
outer diameter($d_o$)=12cm
outer radius($r_o$) = 12/2 = 6 cm

Volume of metal used = volume of outer cylinder - volume of inner cylinder
$V= \pi r_o^2h- \pi r_i^2h\\V= \pi h(r_o^2-r_i^2)\\V= \frac{22}{7} *140(6^2-5^2)\\V= 4840\ cm^3$