Question

The radius and height of a cone are in the ratio 2:5. The area of the base is 154cm². Find its volume .​

Answer 1

Answer:

We have given the ratio of radius and height 4 : 3

Say Radius = 4x

Height = 3x

Slant Height = root [(4x)2 +(3x)2 ]=5x { as it goes to Pythagorean Theorem}

as we know, Area of Base = pie X radius2 =>154=22/7 X 16x2

so solving the eq we get x=1.75cm

Radius=7 , Height =5.25cm, Slant Height =8.75cm

So csa or Curved Surface Area = pie X radius x slant height = 22/7 X 7 X 8.75 x=192.5cm2 (ans)

Step-by-step explanation:

hope it will help you......

Answer 2

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