“A solid consists of a right circular cylinder surmounted by a cone of the same diameter. If the height of the cone is 'h' and the volume of the solid is 3 times the volume of the cone , then find the height of the cylinder.”

If the cylinder's height is H, then we have

1/3 πr^2h + πr^2H = 3 * 1/3 πr^2h
πr^2H = 2/3 πr^2h
H = 2/3 h

A bicycle wheel of radius 35cm is making 25 revolutions in 10secs. At what speed in km/hr is the cyclle moving.

2π*35 cm/rev * 25rev/10s * 1km/100000cm * 3600s/hr = 19.79 km/hr

Thanx man!!😜

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To find the height of the cylinder, let's begin by understanding the volume of the solid and the volume of the cone.

The volume of a cone is given by the formula Vcone = (1/3) * π * r² * hcone, where r is the radius and hcone is the height of the cone.

Let's assume the radius of the cylinder and the cone is 'r'. So, the volume of the cone can be written as Vcone = (1/3) * π * r² * h.

The volume of the solid is given as 3 times the volume of the cone. So, Vsolid = 3 * Vcone.

Let's substitute the value of Vcone into the equation for Vsolid.

Vsolid = 3 * [(1/3) * π * r² * h]
Vsolid = π * r² * h

Now, let's consider the solid which consists of a right circular cylinder surmounted by a cone. The height of the cylinder will be equal to the total height of the solid minus the height of the cone. Let's denote the height of the cylinder as hcylinder.

The total height of the solid is given as 'h', and the height of the cone is also given as 'h'. So, we can write the equation as:

h = hcylinder + hcone
h = hcylinder + h

Now, let's solve for hcylinder.

hcylinder = h - hcone
hcylinder = h - h

Substituting the value of hcylinder in terms of h, the equation becomes:

hcylinder = h - h = 0

Therefore, the height of the cylinder is zero.

This means that the cylinder in the solid has zero height, and it is essentially just a disc with a cone on top.