The radius and height of a cone are in the ratio 2:5. The area of the

1.	The radius and height of a cone are in the ratio 2:5. The area of the base is 154cm². Find its volume .
Answer» Answer: 898.33cm³ Explanation: Given : Ratio of radius and HEIGHT => 2:5. Area of the base => 154cm² To FIND : VOLUME of the cone. Solution : LET the radius and height of the cone be 2x and 5X respectively. We know base area of cone = πr² $\rightarrow \sf{}154cm^2 = \pi\times r^2$ $\rightarrow \sf{}154cm^2 = \dfrac{22}{7}\times2x\times2x$ $\rightarrow \sf{}154cm^2 = \dfrac{22}{7}\times4x^2$ $\rightarrow \sf{}154cm^2 \div \dfrac{22}{7} =4x^2$ $\rightarrow \sf{}49=4x^2$ $\rightarrow \sf{}\dfrac{49}{4}=x^2$ $\rightarrow \sf{}\sqrt{\dfrac{49}{4}}=\sqrt{x^2}$ $\rightarrow \sf{}x=\dfrac{7}{2}$ $\sf{}Radius =>2x$ $\sf{}=>2\bigg(\dfrac{7}{2}\bigg)$ $= >7$ $\sf{}Height =5x$ $\sf{}=>5\bigg(\dfrac{7}{2}\bigg)$ $\sf{}= >\dfrac{35}{2}$ $\sf{}Volume\ of\ the\ cone = \dfrac{1}{3}\pi r^{2}h$ $\sf{}\Rightarrow\dfrac{1}{3}\times\dfrac{22}{7}\times7^2\times\dfrac{35}{2}$ $\sf{}\Rightarrow\dfrac{1}{3}\times\dfrac{11}{1}\times49\times\dfrac{5}{1}$ $\sf{}\Rightarrow\dfrac{11}{3}\times}245$ $\sf{}\Rightarrow\dfrac{2695}{3}$ $\sf{}\Rightarrow 898.33cm^3$ Therefore,volume of the cone is equal to 898.33cm³