An arc of length 22 cm subtends an angle 0 at the centre of a circle. If the radius of the circle is 15 cm, find the value of 0.

The diameter is $13.2 \text{ cm}$.

The height of the tin is $h = 20 \text{ cm}$.

The formula for the volume of a cylinder is $V = \pi r^2 h$.

The tin is half-filled with water.

The correct option is D.

11. Angle subtended by an arc

The formula for arc length is $L = r\theta$, where $L$ is the arc length, $r$ is the radius, and $\theta$ is the angle in radians.
Given $L = 22 \text{ cm}$ and $r = 15 \text{ cm}$.

To convert radians to degrees, multiply by $\frac{180^\circ}{\pi}$. We are given to take $\pi = \frac{22}{7}$.

The correct option is C.

12. Common difference of an Arithmetic Progression

The first term is $a = 20$.
The $n$-th term of an AP is given by $T_n = a + (n-1)d$, where $d$ is the common difference.
The third term is $T_3 = a + (3-1)d = a + 2d$.
The fifth term is $T_5 = a + (5-1)d = a + 4d$.

We are given that the fifth term is four-fifth of the third term:

Substitute $a = 20$ into the equation:

Multiply both sides by 5 to eliminate the fraction:

Subtract $8d$ from both sides and subtract 100 from both sides:

The correct option is D.

13. Rounding to three significant figures

The significant figures are counted from the first non-zero digit.
1st significant figure: 6
2nd significant figure: 0
3rd significant figure: 2

The fourth significant figure is 5.
Since the fourth significant figure (5) is 5 or greater, we round up the third significant figure.

Rounding up the 2 (the third significant figure) makes it 3.
So, 6.02517 rounded to three significant figures is 6.03.

The correct option is B.