Important Formulas: Mensuration

# Important Formulas for CAT Mensuration

## Areas

Areas of some well-known figures are given below:

Example.1 A horizontal pipe for carrying floodwater has a diameter of 1 m. When water in it is 10 cm deep then the width of water surface AB is equal to ________ cm.

(1) 10 cm
(2) 25 cm
(3) 60 cm
(4) 70 cm
(5) None

• Let O be the centre of circle.
⇒ 502 = 402 + x2
⇒ 2500 – 1600 = x2
⇒ x2 = 900
⇒ x = 30
• ∴ AB = 2x = 60 cm.

Question for Important Formulas: Mensuration
Try yourself:The area of quadrilateral PQRS is 228cm2. Find the length of ?.

Example.2 Area of the shaded region is:

## Volume

Length of a Diagonal

• The length of diagonal of a cuboid =
• The length of a diagonal of a cube =

Example.3 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4 circular rounds to reach the top of the building, then what will be total distance (in nearer metres) traveled by insect to reach the top?
(1) 47 m
(2) 48 m
(3) 49 m
(4) 50 m

• Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the pipe.
AO = πd =   = 11m
BO = 5 m
AB =  =  = 12.08 m
• Total distance traveled = 12.08 × 4 = 48.32 m
• Hence distance in nearer meters = 48 m

Question for Important Formulas: Mensuration
Try yourself:What is the volume of a cone having radius of 21cm and height of 5cm?

Example.4 The surface area of a cube is 726 sq metres. Find the volume of the cube
(1) 1234 m2
(2) 1431 m2
(3) 1341 m3
(4) 1331 m3
(5) None of these

• Surface area S = 726 m2 Volume V = ?
• In a cube,
• S = 6a2 = 726 ⇒ a2 = 121 ⇒ a = 11 m
• So, V = a3 = 113 = 1331 m3.
The document Important Formulas for CAT Mensuration is a part of the UPSC Course CSAT Preparation.
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## FAQs on Important Formulas for CAT Mensuration

 1. What is the formula for finding the area of a rectangle?
Ans. The formula for finding the area of a rectangle is length x width.
 2. How do you calculate the volume of a cylinder?
Ans. The formula for calculating the volume of a cylinder is πr^2h, where r is the radius of the base and h is the height of the cylinder.
 3. What is the formula for finding the area of a triangle?
Ans. The formula for finding the area of a triangle is 1/2 x base x height.
 4. How do you calculate the volume of a sphere?
Ans. The formula for calculating the volume of a sphere is 4/3 x π x (radius)^3.
 5. What is the formula for finding the surface area of a cube?
Ans. The formula for finding the surface area of a cube is 6 x (side length)^2.

## CSAT Preparation

194 videos|156 docs|192 tests

### Up next

 Video | 53:29 min
 Doc | 11 pages
 Test | 5 ques
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