Question

The radius of the base of a solid cone is 6 cm and its vertical height is 8 cm. Then the curved surface area (approximate) of the cone in \(\text{cm}^2\) is:

• A. \(186.4\)
• B. \(180.2\)
• C. \(175.3\)
• D. \(188.6\)

Hint:

For cones, always calculate the slant height first using \[ l=\sqrt{r^2+h^2} \] before applying the curved surface area formula \(\pi rl\).

Answer 1

The Correct Option is D

Concept: The curved surface area (CSA) of a cone is given by \[ \text{CSA}=\pi rl \] where \[ r=\text{radius}, \qquad l=\text{slant height} \] and \[ l=\sqrt{r^2+h^2} \] where \(h\) is the vertical height.

Step 1: Find the slant height of the cone. Given \[ r=6\text{ cm}, \qquad h=8\text{ cm} \] Using Pythagoras theorem, \[ l=\sqrt{6^2+8^2} \] \[ =\sqrt{36+64} \] \[ =\sqrt{100} \] \[ =10\text{ cm} \]

Step 2: Substitute into the curved surface area formula. \[ \text{CSA} = \pi rl \] \[ = \pi \times 6 \times 10 \] \[ = 60\pi \]

Step 3: Use the approximate value of \(\pi\). \[ 60\pi \approx 60\times 3.1416 \] \[ = 188.496 \] \[ \approx 188.5 \] Nearest option: \[ \boxed{188.6} \]