A right circular cylinder is one such geometric shape which is used frequently in real life. A cylinder has a closed circular surface having two parallel bases on both the ends. All the points lying on the closed circular surface is at a fixed distance from a straight line known as the axis of the cylinder. The two circular bases of the right angled triangle have same radius and are parallel to each other.

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A surface is generated by a line which intersects a fixed circle and is perpendicular to the plane of the circle is said to be right circular cylinder. A right circular cylinder has two circular bases which are of same radius and are parallel to each other.

Let r be the radius and h be the perpendicular height of a right cylinder as shown below,

The volume of a right cylinder is given by the product of the area of the top or bottom circle and the height of the cylinder. The volume of a right cylinder is measured in terms of cubic units.

Volume = area of the circle $\times$ height of the cylinder

= $\pi r^2$ $\times$ h

= $\pi r^2$ h

**Volume = ****$\pi r^2$ h cubic units**

The sum of lateral surface area and the base area of both the circles will give the surface are of the right circular cylinder.

**Surface area ****= 2 $\pi$ r (h + r) square units**

The surface area of a closed right circular cylinder is the sum of the area of the curved surface and the area of the two bases. The curved surface that joins the two circular bases is said to be lateral surface of the right circular cylinder.

**Lateral area = 2 $\pi$ r h square units**

Volume of a right cylinder = $\pi r^2$ h cubic units

Given that, r = 20 cm

h = 30 cm

Volume = 3.14 $\times$ 20^{2} $\times$ 30

= 3.14 $\times$ 20 $\times$ 20 $\times$ 30

= 37680

So, the volume of the given right cylinder is 37680 cubic cm.

Volume of a right cylinder = $\pi r^2$ h cubic units

Given that, r = 5 m

h = 6.5 m

Volume = 3.14 $\times$ 5^{2} $\times$ 6.5

= 3.14 $\times$ 25 $\times$ 6.5

= 510.25

So, the volume of the given right cylinder is 510.25 cubic m.

Radius of cylinder (r) = 5 cm

Radius of sphere (R) = 10 cm, therefore height of cylinder (h) = 20 cm

From figure: Volume of the shaded region can be found by subtracting the volume of sphere from the volume of cylinder.

=> Volume of the shaded region = Volume of sphere - Volume of cylinder

Volume of sphere = $\frac{4}{3}$ $\pi$ $R^3$

= $\frac{4}{3}$ $\pi$ $\times$ (10)$^3$

= $\frac{4}{3}$ $\pi$$\times$ 1000

= 1333.33$\pi$

Volume of cylinder = $\pi$ $r^2$ h

= $\pi$(25)(20)

= 500$\pi$

Now,

Volume of the shaded region = 1333.33$\pi$ - 500$\pi$

= 833.33 $\pi$

Using $\pi$ = 3.14 and rounding to the nearest tenth, we get

Volume = 833.33 $\times$ 3.14 = 2616.65

Hence, the Volume of the shaded region is 2616.65 cm^{3}

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