Ncert Exercises & Solutions

Choose the incorrect statement from the given ones:

1.	The volume of a cube of side $1~\text{cm}$ is equal to $10^{-6}~\text{m}^2$.
2.	The surface area of a solid cylinder of radius $2.0~\text{cm}$ and height $10~\text{cm}$ is equal to $1.5\times10^{4}~\text{mm}^2$.
3.	A vehicle moving with a speed of $18~\text{km/h}$ covers $5~\text m$ in $1~\text s$.
4.	The relative density of lead is $11.3$. Its density is $11.3~\text{g/cm}^3$.

(a)

As we know, 1 m = 100 cm

So, 1 cm = 1/100 m= $10^{- 2} m$

The volume of the cube = 1 cm × 1 cm × 1 cm = $= 10^{- 2} \times 10^{- 2} \times 10^{- 2} m^{3} = 10^{- 6} m^{3}$

Hence, the volume of a cube of side 1 cm is equal to $10^{- 6} m^{3}$ .

(b) The total surface area of a cylinder of radius r and height h,

S = 2 $π$ r(r + h).

Given that, r = 2 cm = 2 × 1 cm = 2 × 10 mm = 20 mm

h = 10 cm = 10 × 10 mm = 100 mm

$\Rightarrow S = 2 \times 3.14 \times 20 \times (20 + 100) = 15072 = 1.5 \times 10^{4} {mm}^{2}$

1 km/h = $\frac{5}{18} m / s$

$18 km / h = 18 \times \frac{5}{18} = 5 m / s$

Therefore, distance can be obtained using the relation:

Distance = Speed × Time = 5 × 1 = 5 m

Hence, the vehicle covers 5 m in 1 s.

(d)The relative density of a substance is given by the relation,

Relative density = $\frac{Density of substance}{Density of water}$

The density of water = 1 $g / {cm}^{3}$

The density of lead = Relative density of lead $\times$ Density of water
= 11.3 x 1 = 11.3 $g / {cm}^{3}$

Again, 1g = $\frac{1}{1000} kg$

$1 {cm}^{3} = 10^{- 6} m^{3}$

$1 g / {cm}^{3} = \frac{10^{- 3}}{10^{- 6}} kg / m^{3} = 10^{3} kg / m^{3}$

$\Rightarrow 11.3 g / {cm}^{3} = 11.3 \times 10^{3} kg / m^{3}$

1.	The volume of a cube of side \(1~\text{cm}\) is equal to \(10^{-6}~\text{m}^2\).
2.	The surface area of a solid cylinder of radius \(2.0~\text{cm}\) and height \(10~\text{cm}\) is equal to \(1.5\times10^{4}~\text{mm}^2\).
3.	A vehicle moving with a speed of \(18~\text{km/h}\) covers \(5~\text m\) in \(1~\text s\).
4.	The relative density of lead is \(11.3\). Its density is \(11.3~\text{g/cm}^3\).