#### To determine

a)

**To prove:**

Cavalier’s Principle

#### Answer

S1=S2

#### Explanation

**1) Concept:**

Cross sections of two solids parallel plane are equal, then use integration by using cross section of each solid.

**2) Calculation:**

Let A_{1} is cross sectional area of two solids in first plane and dx is the distance of second parallel plane from the first plane.

Therefore first term in the volume is ∫A1dx

Let A_{2} is cross sectional area in second plane

Then next term in the volume is ∫A2dx

Every volume term is same on both sides.

Therefore, volume of S1= ∫A1dx+A2dx+…..Andx= ∫A1+A2+……+Andx

volume of S2= ∫A1dx+A2dx+…..Andx= ∫A1+A2+……+Andx

Therefore, S1=S2

**Conclusion:**

If the family of parallel planes gives equal cross section areas for two solids, then their volume is also the same.

#### To determine

b)

**To find:**

Volume of oblique cylinder

#### Answer

πr2h

#### Explanation

**1) Concept:**

Cavalier’s Principle

If a family of parallel planes gives equal cross-sectional areas for two solids *S* 1 and *S* 2, then the volumes of *S* 1 and *S* 2 are equal

**2) Calculation:**

Consider a right circular cylinder of same height and base as that of given oblique cylinder.

So, by cavalier’s principle, as two solids having same area of base and height, there volume is also same.

So find the volume of cylinder,

V=Bh

Here B is area of base which is area of circle and height is h

Area of circle is,

A=πr2=B

So volume of cylinder is,

V=πr2h

Hence, volume of oblique cylinder is πr2h

**Conclusion:**

Therefore, V=πr2h