The radii of the top and bottom of a bucket (frustum) are 28 cm and 7 cm, and its slant height is 45 cm. The curved surface area is
4950 cm²
4951 cm²
4952 cm²
4953 cm²
Step 1: Recall the formula for the curved surface area (CSA) of a frustum of a cone:
\[ CSA = \pi (R + r) l \]
where:
Step 2: Substitute the given values:
\(R = 28\,\text{cm},\; r = 7\,\text{cm},\; l = 45\,\text{cm}\)
Step 3: Add the radii:
\(R + r = 28 + 7 = 35\)
Step 4: Multiply with slant height:
\((R + r) \times l = 35 \times 45 = 1575\)
Step 5: Multiply with \(\pi\) (take \(\pi = 3.1416\)):
\(CSA = 1575 \times 3.1416 \approx 4949.98\,\text{cm}^2\)
Step 6: Round off to the nearest whole number:
\(CSA \approx 4950\,\text{cm}^2\)
Final Answer: The curved surface area is 4950 cm².