The diagram shows a flowerpot in the shape of a frustum of a cone. The diameters of the top and bottom ends are 64cm and 48cm respectively. If the slant height is 15cm, calculate the curved surface area of the pot.

Here are the solutions to the problems:

: Curved surface area of a frustum

The diagram shows a flowerpot in the shape of a frustum of a cone. The diameters of the top and bottom ends are 64 cm and 48 cm respectively. If the slant height is 15 cm, calculate the curved surface area of the pot.

Step 1: Identify the radii and slant height.
Top diameter $= 64 \text{ cm} \implies \text{Top radius } (R) = \frac{64}{2} = 32 \text{ cm}$.
Bottom diameter $= 48 \text{ cm} \implies \text{Bottom radius } (r) = \frac{48}{2} = 24 \text{ cm}$.
Slant height $(l) = 15 \text{ cm}$.

Step 2: Apply the formula for the curved surface area of a frustum.
The formula for the curved surface area of a frustum is $A = \pi (R + r) l$.
Using $\pi = \frac{22}{7}$ as in previous problems:

$$A = \frac{22}{7} (32 + 24) (15)$$ $$A = \frac{22}{7} (56) (15)$$

Step 3: Calculate the area.

$$A = 22 \times \left(\frac{56}{7}\right) \times 15$$ $$A = 22 \times 8 \times 15$$ $$A = 176 \times 15$$ $$A = 2640 \text{ cm}^2$$

The curved surface area of the pot is $\boxed{2640 \text{ cm}^2}$.

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The table below shows the distribution of marks of candidates in an examination.