Answer

Verified

450.3k+ views

__Hint:__Hypotenuse is the longest side of a right-angled triangle so it is obvious when the question says the triangle revolved around its sides, it means the sides with length 3 cm and 4 cm. Therefore, for the two cones that form:

1) First cone: Height = 4 cm, Radius of base = 3 cm

2) Second cone: Height = 3 cm, Radius of base = 4 cm

Drawing a diagram is helpful in case you are unable to visualize the cones.

Here in the figure we have shown the triangle which has revolved about the two of its side and the two cones formed. Cone (a) is formed when the triangle is revolved around the 4 cm side and (b) is the cone when the triangle is revolved around 3 cm of the side.

Now, try to solve the question by yourself before looking at the complete solution.

__Complete step-by-step answer:__As we know the right angled triangle can be revolved from $3cm\,\,\& \,\,4cm$.

Since the sides making the right angle are $3cm{\text{ and }}4cm$.

When it is revolved about the side of length ${\text{3}}cm$ then the radius of the cone is ${\text{3}}cm$ and the height of the cone is $4cm$.

Then the volume of the cone is,

$\dfrac{1}{3}\pi ({3^2})(4) = 12\pi \,\,\,\,\,\,...({\text{i}})$

When it is revolved about the side of length $4cm$ then the radius of the cone is $4cm$ and the height of the cone is $3cm$.

Then the volume of the cone is,

$\dfrac{1}{3}\pi ({4^2})(3) = 16\pi \,\,\,...{\text{(ii)}}$

Subtracting (i) from (ii) we get,

${\text{16}}\pi {\text{ - 12}}\pi {\text{ = 4}}\pi $

Hence the answer is $4\pi $.

__Note:__In this problem we have revolved the right angled triangle about the sides other than hypotenuse. Since those are the sides, if we revolve the triangle around them we will get two cones of different volume. Then the side about which the triangle is revolved will become the radius of the cone and the side other than hypotenuse will be the height of the cone. Then after finding their volume we subtract the both volumes to get the solution to this problem. The slant height of the cone will be the same in both the cases since it is hypotenuse.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How many crores make 10 million class 7 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths