Q. 17

# Two steel sheets each of length *a*_{1} and breadth *a*_{2} are used to prepare the surfaces of two right circular cylinder —one having volume *v*_{1} and height *a*_{2} and other having volume *v*_{2} and height a_{1.} Then,

A. *v*_{1}=*v*_{2}

B. *a*_{2}*v*_{1}=*a*_{1}*v*_{2}

C. *a*_{1}*v*_{1}=*a*_{1}*v*_{2}

D.

Answer :

In case (i)

2πr= a_{1}

= r = a_{1}/2π

= h_{1} = a_{2}

So, v_{1} = πr^{2}h = π×(a_{1}/2π)^{2}h = a_{1}^{2}a_{2}/4π…………..(1)

In case (ii)

2πr = a_{2}

= r = a_{2}/2π and h = a_{1}

So, v_{2} = πr^{2}h = π× (a_{2}/4π)^{2}a_{1} = a_{2}^{2}a_{1}/4π……………….(2)

From equations 1 and 2 …

= a_{2}v_{1} = a_{1}v_{2}

= v_{1/}a_{1} = v_{2}/a_{2} ( so both options (B) and (D) are correct.)

Rate this question :

If the radius of a cylinder is doubled and the height remains same, the volume will be

RD Sharma - MathematicsIf each edge of a cube, of volume *V,* is doubled, then the volume of the new cube is

The height *h* of a cylinder equals the circu,ference of the cylinder. In terms of *h*, what is the volume of the cylinder?

Find the lateral surface area and the total surface area of a cube of side 8 cm.

RS Aggarwal & V Aggarwal - MathematicsThe volume of a cube is 512 cm^{3}. Its total surface area is