Question

Fill in the blanks 

1. The volume of a cube of side 1 cm is equal to________\(m^3\).
2. The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to__________\(\text(mm)^2\).
3. A vehicle moving with a speed of 18 km \(h^{-1}\) covers ________m in 1 s.
4. The relative density of lead is 11.3. Its density is ....g \(\text {cm}^{-3}\) or ________kg \(\text m^{-3}\).

Answer 1

a. The volume of a cube of side 1 cm is equal to \(\underline{10^{-6}\;\text m^3}.\)
explanation: 
1 cm =\(\frac{1}{100}\)m
Volume of the cube = 1 \(\text{cm}^3\)
But, 1 \(\text{cm}^3\) = 1 cm × 1 cm × 1 cm = \(\bigg(\frac{1}{100}\bigg)\)m × \(\bigg(\frac{1}{100}\bigg)\)m × \(\bigg(\frac{1}{100}\bigg)\)m
\(\therefore\) 1 \(\text{cm}^3\) = \(10^{-6}\;\text m^3\)
Hence, the volume of a cube of side 1 cm is equal to \(10^{-6}\;\text m^3\) .

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b. The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to \(\underline{1.5 \times10^4 \;\text {mm}^2}.\)
explanation: 
The total surface area of a cylinder of radius r and height h is S = 2\(\pi\)r (r + h).
Given that, r = 2 cm = 2 × 1 cm = 2 × 10 mm = 20 mm
h = 10 cm = 10 × 10 mm = 100 mm 
\(\therefore\) S = 2× 3.14 × 20 × (20 + 100) = 15072 = 1.5 × \(10^4 \;\text {mm}^2\)

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c. A vehicle moving with a speed of 18 km \(h^{-1}\) covers \(\underline{5\;\text m\;\text in \;1 \text s.}\)
explanation: 
Using the conversion, 1 km/h =\(\frac{5}{18}\) m / s
18 km / h = 18 ×\(\frac{5}{18}\)= 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.

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d. The relative density of lead is 11.3. Its density is \(\underline{11.3\;\text{g}/\text{cm}^3}\) or \(\underline{11.3\times10^3\; \text{kg}/\text m^3}.\)
explanation: 
Relative density of a substance is given by the relation, 
Relative density =\(\frac{ \text{Density of substance}}{ \text{Density of water}}\)
Density of water = 1 \(\text{g}/\text{cm}^3\)
Density of lead = Relative density of lead × Density of water = 11.3 × 1 = 11.3 \(\text{g}/\text{cm}^3\)

Again , 1g =\(\frac{1}{1000}\) kg

1 \(\text{cm}^3\) = \(10^{-6}\;\text m^3\)
1 \(\text{g}/\text{cm}^3\) = \(\frac{10^{-3}}{10^{-6}}\) kg/ \(\text m^3\) = \(10^3\; \text{kg}/\text m^3\)
\(\therefore\) 11.3 \(\text{g}/\text{cm}^3\) = 11.3 ×\(10^3\; \text{kg}/\text m^3\)