can anyone suggest me ways and tricks to solve mensuration questions easily QUALITY ANSWER NEEDED!!!!!!!!
Answers
Answer:
Mensuration as a whole is a formula oriented topic where most mensuration problems can be solved by using the appropriate formulas. After discussing introduction to mensuration with a list of mensuration formulas and how to solve mensuration problems on area and perimeter, it’s time to move to the third and last part of this series on mensuration where we discuss mensuration problems on volume and surface area. In the third post in series on mensuration problems we will be discussing volume and surface area based mensuration problems on 3D shapes. So go through the list of formulas and gear up for questions on volume and surface area that are asked inIBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams.
The Mensuration problems on volume and surface area of 3D shapes is divided in 3 parts- Basic Problems, Problems on Lateral and Curved Surface Area and finally, Problems on Proportionality of Volume.
Set I: Basic Mensuration Problems on Volume and Surface Area
Questions discussed in this part involve basic usage of the volume and surface area formula with a little bit of modification.
Problem 1: The volume of a circular cone is 100p cm3 and its height is 12cm. What is the slant height?
Solution 1:
Surely you know the formula to find the slant height and the volume of a circular cone-
Volume and Surface Area
Volume and Surface Area
From the diagram we know that ‘l’ is the slant height. To find ‘l’ we need to know the radius and the height of the cone. Once we have these two, we can easily use the hypotenuse formula get the value of ‘l’ since the three for a right-angled triangle. We already have the height of the cone so we just need to find the radius of the cone.
Step 1
We know the formula for the volume of a cone-
Volume of a Cone = (1/3)pr2 h cubic Units (i)
Volume of a Cone = 100p cm3 (ii)
Step 2
Both Equation (i) and (ii), since both of them
(1/3)pr2 h = 100p
Putting the value of height and cancelling p on both the ends we get –
(1/3)r2 x 12 = 100
r2 = (100 x 3) / 12
r2 = 25
r = 5
So the radius of the circular cone is 5cm
Step 3
Now that we know the value of both, height and radius, we can simply put the values in the formula and get the value of ‘l’.
Slant Height of cone, l = Ö{h2+r2}
Slant Height of cone, l = Ö{122+52}
Slant Height of cone, l = Ö{144+25}
Slant Height of cone, l = Ö169
Slant Height of cone, l = 13
So the slant height of the circular cone is 13cm.
So every time you see a question like this, go through the list of formulas of volume and surface area of the given shape in your head and solve such mensuration problems.
Set II: Mensuration Problems on Lateral and Curved Surface Area
Volume and surface area problems discussed in this set are about the interiors of closed 3D shapes. The trick to solve such questions on volume and surface area, lies in being able to identify the right formula and then use in to get values of the needed parameters based on the values that you and have and the finally get the correct answer.
Problem 1: All the four lateral walls and the ceiling of a room of length 12 feet, breadth 10 feet and height 8 feet are to be painted. Find the total cost, if the cost of painting is Rs 15/sq. feet and the doors and windows in the room occupy 40 sq. feet of the area.
Solution 1:
From the information given in the question, we infer that the 3D shape here is a cuboid. The four walls and the ceiling need to be painted sans the area occupied by the doors and windows. We can have two different approaches to find this area.
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The Lateral Surface Area will include the area covered by the walls on all the four sides. We can find the Lateral Surface Area, add the area of the roof and from this total subtract the area occupied by doors and windows.
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The Total Surface Area will include the area of all the four walls, the floor and the roof. We can take the total surface area of the room and from that subtract the area of the floor and the area occupied by doors and windows.
In both these cases we will get the total area in the room that is to be painted.