WORD PROBLEMS
RELATED TO MENSURATION
FOR CLASS 8TH , 9TH ,10TH
Q 1.] A fixed open cylindrical metal tank having radius 4.9m and height 7.5m is to be painted from inside and outside . What will it cost at the rate of rupees 10 per m2 ?
Solution : Fixed Open Cylindrical Metal Tank
Given :
Radius = r= 4.9m Height = h = 7.5 m Rate of painting = Rs. 10 per m2
Find the cost of painting the inside and outside of the tank =?
Step 1)
Area of the inside of the tank = lateral surface area + area of its circular base
= (2 * pie * r * h) + (pie * r2)
= pie * r * (2 * h + r)
= 22/7 * 4.9 ( 2 * 7.5 + 4.9 )
= 22/7 * 4.9 ( 15 + 4.9 )
= 22/7 *4.9 * 19.9
=306.46 m2
Step 2)
Similarly, Area of the outside of the tank = 306.46m2
step 3) Total inside and outside area of the tank to be painted = 306.46m2 + 306.46m2
= 612.92 m2
Step 4) Total cost of painting = 612.92 * 10 = Rs. 6129.2
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Q.2) Find the ratio of the total surface area and the curved surface area of a right circular cylinder given that its height and radius are 9 m and 2.1m respectively.
SOLUTION : RIGHT CIRCULAR CYLINDER
GIVEN : Height = h = 9 m radius = r = 2.1 m
Find the ratio of the total surface area and curved surface area = ?
i.e. TSA : CSA = ?
TSA / CSA = 2 * Pie * r ( h + r ) /2 * pie * r * h
= ( h + r ) / h
= ( 9 + 2.1 ) / 9
= 11.1 /9
= 111 /90
= 37/30
= 37 : 30
Ans : The ratio of TSA : CSA is 37:30
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Q.3) A cylindrical shaped packaging for a brand of biscuits has red colour paint in the center leaving a margin of 7 cm from top and bottom each . Find the area painted red if the diameter 0f packaging is 10.5 cm and its is 25 cm high.
SOLUTION : CYLINDRICAL SHAPED PACKAGING
GIVEN : diameter = 10.5 cm radius = r = 10.5 /2 cm
height = 25 cm
leaving a margin from top and bottom = 7 cm
height of the red colour in the center = 25 – 7 -7 = 11 cm
Find the area painted red =?
Area of the area painted red = 2 * pie * r * h
= 2 * 22/7 * 10.5/2 * 11
= 363 cm2
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Q.4) A cuboidal tank with dimensions 5m * 2m * 4m is filled with water. How many litres of water is there in the tank ? If 2500 buckets of 9.6 L each are filled from the water tank, how much water will be left ?
SOLUTION : CUBOIDAL TANK
GIVEN : Length = l = 5mBreadth = b = 2m Height = h= 4m
Step 2)
Volume of water = l * b * H = 5 * 2 * 4 =40 m3
= 40 * 1000 ( 1 m3 = 1000 L)
Step 3)
No. of buckets = 2500 Capacity of each bucket = 9.6 L
Capacity of 2500 buckets = 2500 * 9.6 = 24000
Step 4)
Water will be left = 40,000 – 24000 = 16000L
Ans : 16000 L of water will be left in the tank.
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Q.5) A metal cube is melted to form three smaller cubes of edges 3cm, 4cm and 5 cm. Find the edge of the original metal cube.
SOLUTION : THREE SMALLER CUBES
GIVEN : edge of the 1st cube = 3 cm
edge of the 2nd cube = 4 cm
edge of the 3rd cube = 5 cm
Find the edge of the original metal cube = ?
Step 1)
Volume of the 1st cube = a3 = 3 * 3 *3 = 27 cm3
Volume of the 2nd cube = a3 = 4 *4 * 4 = 64cm3
Volume of the 3rd cube = a3 = 5 * 5 * 5 = 125 m3
Step 2)
Volume of the original metal cube = 27 + 64 + 125 = 216 cm3
Step 3)
Volume of the original metal cube = a3
216 = a3
6 cm = a
Ans : The edge of the original metal cube is 6cm.
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Q.6) A cube of edge 11 cm is melted and formed into a cylindrical wire of diameter 0.5 cm. What length of wire will be obtained from the cube ?
SOLUTION : CUBE CYLINDRICAL WIRE
edge = a = 11 cm diameter =d = 0.5 cm radius = r = 0.5 /2 cm
Find the length of the wire obtained from the cube = Height = h = ?
Step 1)
Volume of the cube = a3 = 11 * 11 * 11 = 1331 cm3
Step 2)
Volume of the cube = Volume of the wire = pie * r2 * h
1331 = 22/7 * 0.5/2 * 0.5/2 * h
1331 *7/22 * 2/0.5 * 2/0.5 = h
37268 /5.5 = h
6776 cm = h
Ans : The length of the wire obtained is 6776 cm .
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