Question : The curved surface area is thrice as big as the base area of a cone. If the diameter of the cone is 1 cm. Then what is the total surface area (in cm2) of the cone?
Option 1: $\pi$
Option 2: $3\pi $
Option 3: $2\pi$
Option 4: $4\pi $
Correct Answer: $\pi$
Solution :
Let the radius of the cone as $r$, the slant height as $l$, and the height as $h$.
Given that the diameter of the cone is 1 cm, the radius r is half of the diameter, which is 0.5 cm.
The base area $A$ of a cone,
$A = \pi r^2$
Substituting $r$ = 0.5 cm into the formula.
$⇒A = \pi (0.5)^2 = 0.25\pi ~\text{cm}^2$
Given that the curved surface area is thrice as big as the base area, the curved surface area $L$ is,
$⇒L = 3A = 3 \times 0.25\pi = 0.75\pi \, \text{cm}^2$
The total surface area of a cone is the sum of the base area and the curved surface area.
Total surface area $= A + L = 0.25\pi +0.75\pi=\pi~\text{cm}^2$
Hence, the correct answer is $\pi$.
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