A solid body consists of a cylinder surmounted by a hemisphere of the same radius. The total length of the body, measured along the central axis of cylinder, is 10cm. If the radius of the hemisphere is xcm
To find the value of x, we need to consider the dimensions and geometry of the solid body. Let's break it down step by step:
1. The total length of the body is given as 10cm. This length is measured along the central axis of the cylinder.
2. The solid body consists of a cylinder and a hemisphere.
3. The cylinder is surmounted (placed on top of) by the hemisphere. This means that the base of the hemisphere is attached to the top of the cylinder, and they share the same central axis.
4. The radius of the hemisphere is given as x cm.
Now, let's calculate the length of the cylinder and the hemisphere separately:
1. Cylinder:
The length of the cylinder can be calculated by subtracting the height of the hemisphere from the total length of the body. Since both the cylinder and the hemisphere share the same central axis, the height of the hemisphere is also the radius of the hemisphere.
Cylinder Length = Total Length - Hemisphere Height
= 10 cm - x cm
= 10 - x cm
2. Hemisphere:
The height of the hemisphere is equal to its radius, which is also given as x cm.
Now, we can write an equation to find the value of x:
Total Length = Cylinder Length + Hemisphere Height
10 cm = (10 - x) cm + x cm
10 = 10 - x + x
10 = 10
From the equation above, we can see that x cancels out, and both sides of the equation are equal. This means that the value of x can be any real number.
Therefore, we have determined that the value of x is not specific and can be any real number.