The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area
Question 1 Report
The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area
Answer Details
The curved surface area of a cone is given by the formula:
\[\text{Curved surface area} = \pi rl,\]
where $r$ is the radius of the base, $l$ is the slant height, and $\pi$ is the constant pi (approximately 3.14).
In this case, the height of the cone is 4 cm and the radius of the base is 3 cm. To find the slant height, we can use the Pythagorean theorem:
\[l^2 = r^2 + h^2.\]
Plugging in the values we get,
\[l^2 = 3^2 + 4^2 = 9 + 16 = 25.\]
So, $l = 5$ cm.
Now, we can use the formula for curved surface area, substituting $r=3$ cm and $l=5$ cm:
\[\text{Curved surface area} = \pi \cdot 3 \cdot 5 = 15\pi \text{ cm}^2.\]
Therefore, the answer is (B) $15\pi cm^2$.
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