Question

Fill in the blanks

(a) The volume of a cube of side $1cm$ is equal to ________ $m^3$

(b) The surface area of a solid cylinder of radius $2.0cm$ and height $10.0cm$ is equal to ________ $(mm{)}^2$

(c) A vehicle moving with a speed of $18km/h$ covers ________ metres in one second.

(d) The relative density of lead is $11.3$. Its density is ________ $g/c{m}^3$ or ________$kg/m^3$

Answer 1

(a)

$1m=100cm$

$1cm=0.01m$
$Volume=(1cm{)}^3$
$=(0.01m{)}^3$
$={10}^{-6}{m}^3$

(b)

Surface Area of cylinder $=$ Curved Area + Area of top + Area of Base
$=2\pi rh+\pi r^2+\pi r^2$
$=2\pi r(r+h)$
Given:

$r=2cm=20mm$
$h=10cm=100mm$
Surface area $=2\pi r(r+h)=2\times 3.14\times 20(20+100)m{m}^2$
$=15072m{m}^2$

(c)

Speed $=18km/hr$
Converting to $m/s$
$1km=1000m$
$1hr=(60\times 60)s=3600s$
$1km/h=\frac{1000m}{3600s}=\frac{5}{18}m/s$
$18km/h=5m/s$
Distance travelled in $1s=5m$

(d)

Relative density $=\frac{Density}{Densityofwater}=\frac{\rho }{{\rho }_w}$
${\rho }_w=1000kg/m^3$
Relative density $=11.3$
$\frac{\rho }{1000}=11.3$
$\rho =11.3\times 1000kg/m^3$

Now,
$1kg=1000g$
$1m=100cm$
Putting in $\rho$
$\rho =1.13\times {10}^{4}kg/m^3=1.13\times {10}^4\times \frac{1000g}{{100}^{3}c{m}^3}=11.3g/c{m}^3$