Question : The perimeter of the base of a right circular cone is 44 cm. If the height of the cone is 24 cm, then what is the curved surface area (in cm2) of the cone?
Option 1: 550
Option 2: 1100
Option 3: 2200
Option 4: 650
Correct Answer: 550
Solution : The perimeter of the base of a right circular cone is given as 44 cm. The circumference of the base = $2\pi r$, where $r$ is the radius of the base. $⇒2\pi r=44$ $⇒r = \frac{44}{2\pi}=\frac{22}{\pi}=\frac{22×7}{22}=7\;\mathrm{cm}$ $⇒l = \sqrt{r^2 + h^2}$ $⇒l = \sqrt{(7\;\mathrm{cm})^2 + (24\;\mathrm{cm})^2}$ $⇒l=25\;\mathrm{cm}$ The curved surface area of a cone $ = \pi rl$ The curved surface area of a cone = $\frac{22}{7}$ × 7 × 25 The curved surface area of a cone = 550 cm2 Hence, the correct answer is 550.
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Question : The perimeter of the base of a right circular cone is 132 cm. If the height of the cone is 72 cm, then What is the total surface area (in cm2) of the cone?
Option 1: 6600
Option 2: 6336
Option 3: 4224
Option 4: 5784
Question : The curved surface area and circumference at the base of a solid right circular cylinder are 2200 cm2 and 110 cm, respectively. Find the height of the cylinder.
Option 1: 24 cm
Option 2: 22 cm
Option 3: 20 cm
Option 4: 18 cm
Question : If the area of the base of a cone is 154 cm2 and the area of its curved surface is 550 cm2, then its volume is:
Option 1: 1232 cm3
Option 2: 1122 cm3
Option 3: 1434 cm3
Option 4: 1535 cm3
Question : The radius of a right circular cone is 3 cm and its height is 4 cm. The total surface area of a cone is:
Option 1: 48.4 cm2
Option 2: 64.4 cm2
Option 3: 96.4 cm2
Option 4: 75.4 cm2
Question : The curved surface area of a cone whose base radius is 7 cm and slant height is 10 cm is:
Option 1: 280 cm2
Option 2: 250 cm2
Option 3: 300 cm2
Option 4: 220 cm2
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