Question : The radius and height of a right circular cone are in the ratio 1 : 2.4. If its curved surface area is 2502.5 cm2, then what is its volume? (Take $\pi=\frac{22}{7}$)
Option 1: 8085 cm3
Option 2: 8820 cm3
Option 3: 11550 cm3
Option 4: 13475 cm3
Correct Answer: 13475 cm3
Solution : The ratio of the radius and height of a right circular cone = 1 : 2.4 = 10 : 24 = 5 : 12 Let radius, $r = 5x$, height, $h=12x$ and slant height be $l$. $l^2 = r^2 + h^2 = (5x)^2 + (12x)^2 = 25x + 144x = 169x^2$ ⇒ $l = \sqrt{169x^2}=13x$ Curved surface area of a cone = $\pi r l$ ⇒ $2502.5 = \frac{22}{7} × 5x × 13x$ ⇒ $x^2 = \frac{2502.5 × 7}{22 × 5 × 13} = 12.25$ ⇒ $x = 3.5$ Now, the volume of a cone = $\frac{1}{3}\pi r^2h$ = $\frac{1}{3}×\frac{22}{7}×(5x)^2×12x$ = $\frac{1}{3}×\frac{22}{7}×25× 3.5^2 ×12×3.5$ = 13475 cm3 Hence, the correct answer is 13475 cm3.
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Question : The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm3?
Option 1: $192 \pi$
Option 2: $210 \pi$
Option 3: $240 \pi$
Option 4: $180\pi$
Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
Question : What is the difference between the total surface area and the curved surface area of a cone whose radius is 35 cm? (Take $\pi=\frac{22}{7}$)
Option 1: 3850 cm2
Option 2: 3704 cm2
Option 3: 3750 cm2
Option 4: 3675 cm2
Question : The radius of the base of a cylinder is 14 cm and its curved surface area is 880 cm2. Its volume (in cm3) is: (Take $\pi=\frac{22}{7}$)
Option 1: 3080
Option 2: 1078
Option 3: 6160
Option 4: 9240
Question : The radius of the base of a cylinder is 14 cm and its volume is 6160 cm3. The curved surface area (in cm2) is: (Take $\pi=\frac{22}{7}$)
Option 1: 778
Option 2: 880
Option 3: 660
Option 4: 940
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