# Shortcut Method To Solve Mensuration - 2

## Effective for IBPS PO - SBI PO Exam

Here we will start a series of Quantitative Aptitude Shortcut Tricks for your upcoming SBI - IBPS - SSC and Other Government Competitive Exams. We will try to cover up all topics of the quantitative Aptitude Sections from which question was generally asked.

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Trick - 1

• If a circular wire of radius x units is cut and bent in the form of a rectangle whose sides are in the ratio of a:b, then the sides of the rectangle are given by

$\left[ \pi x\left( \frac{a}{a+b} \right) \right]units$  and $\left[ \pi x\left( \frac{b}{a+b} \right) \right]units$

Trick - 2
• If the radius of a right circular cylinder is changed by x % and height is changed by y%, then curved surface area changes by

$\left[ x+y+\frac{xy}{100} \right]percent$
Trick - 3
• If radius of a right circular cylinder is changed by x % and height is changed by y% then volume changes by

$\left[ 2x+y+\frac{{{x}^{2}}+2xy}{100}+\frac{{{x}^{2}}y}{{{100}^{2}}} \right]percent$
Trick - 4
• If radius of a right circular cylinder is changed by x % and height remains the same the volume changes by

$\left[ 2x+\frac{{{x}^{2}}}{100} \right]percent$ or $\left[ {{\left( 1+\frac{x}{100} \right)}^{2}}-1 \right]\times100 percent$
Trick - 5
• If height and radius of a right circular cylinder both changes by x%, then volume changes by
$\left[ 3x+\frac{3{{x}^{2}}}{100}+\frac{{{x}^{3}}}{{{100}^{2}}} \right]percent$
Trick - 6
• If side of a cube is increased by x% then its surface area increases by
$\left( 2x+\frac{{{x}^{2}}}{100} \right)percent$

Questions for Practice

Q1.  A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6 : 5. Find the smaller side of the rectangle.

Q2. The radius and height of a cylinder are increased by 10 % and 20% respectively. Find the percent increase in its curved surface area.

Q3. The radius  of a right circular cylinder is decreased by 10% but its height is increased by 15%. What is the percentage change in its volume ?

Q4.  The radius  of a cylinder is  increased by 25 %. Keeping its height unchanged. What is the percentage increase in its volume ?

Q5.  Each of the radius and the height of a right circular cylinder is both increased by 10%. Find the % by which the volume increases.

Q6. Each edge of a cube is increased by 50%. What is the percentage increase in its volume ?