Step-by-step explanation:
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→154cm
2
=π×r
2
\rightarrow \sf{}154cm^2 = \dfrac{22}{7}\times2x\times2x→154cm
2
=
7
22
×2x×2x
\rightarrow \sf{}154cm^2 = \dfrac{22}{7}\times4x^2→154cm
2
=
7
22
×4x
2
\rightarrow \sf{}154cm^2 \div \dfrac{22}{7} =4x^2→154cm
2
÷
7
22
=4x
2
\rightarrow \sf{}49=4x^2→49=4x
2
\rightarrow \sf{}\dfrac{49}{4}=x^2→
4
49
=x
2
\rightarrow \sf{}\sqrt{\dfrac{49}{4}}=\sqrt{x^2}→
4
49
=
x
2
\rightarrow \sf{}x=\dfrac{7}{2}→x=
2
7
\sf{}Radius = > 2xRadius=>2x
\sf{}= > 2\bigg(\dfrac{7}{2}\bigg)=>2(
2
7
)
= > 7=>7
\sf{}Height =5xHeight=5x
\sf{}= > 5\bigg(\dfrac{7}{2}\bigg)=>5(
2
7
)
\sf{}= > \dfrac{35}{2}=>
2
35
\sf{}Volume\ of\ the\ cone = \dfrac{1}{3}\pi r^{2}hVolume of the cone=
3
1
πr
2
h
\sf{}\Rightarrow\dfrac{1}{3}\times\dfrac{22}{7}\times7^2\times\dfrac{35}{2}⇒
3
1
×
7
22
×7
2
×
2
35
\sf{}\Rightarrow\dfrac{1}{3}\times\dfrac{11}{1}\times49\times\dfrac{5}{1}⇒
3
1
×
1
11
×49×
1
5
\sf{}\Rightarrow\dfrac{11}{3}\times}245
\sf{}\Rightarrow\dfrac{2695}{3}⇒
3
2695
\sf{}\Rightarrow 898.33cm^3⇒898.33cm
3
Therefore,volume of the cone is equal to 898.33cm³