Math Mensuration Made Great : With Word Problems For Class 8th,9th,10th[16]

Q.1) Find the volume of a cuboid whose length is 12m, breadth is 9m and height is 6.5m.

SOLUTION:

Given:
Length = L = 12m
Breadth = B = 9m
Height = H = 6.5m

Volume of the cuboid = L * B * H = 12 * 9 * 6.5 = 702 m³
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Q.2) Find the volume of a cubical box whose edge is 8cm.

SOLUTION:

Given:
Measure of each edge of cubical box = 8cm

Volume of the box = (Edge)³ = (8cm)³ = 512cm³

Hence, the volume of the cubical box is 512cm³.
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Q.3) The volume of a cuboidal box is 168m³. If it is 6m long and 3.5m high, find its width.

SOLUTION:

Given:
Volume of cuboidal box = V = 168m³
Length of cuboidal box = L = 6m
Height of cuboidal box = 3.5m

Let the breadth of the cuboidal box be x m.

Then volume of the box = 168
L * B * H = 168
6 * x * 3.5 = 168
x = 168 / 6 * 3.5
x = 8m

Hence, the width of the box is 8m.
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Q.4) The volume of a cube is 343m³. Find its total surface area and lateral surface area.

SOLUTION:

Given:
Volume of the cube = 343cm³ [ Given ]
(Side)³ = 343cm³ [ Volume of the cube = (Side)³ ]


(Side)³ = 343cm³
(Side)³ = 7³ cm³
Side = 7cm

Total surface area of the cube = 6 * (Side)²
= ( 6 * 7² ) cm²
= ( 6 * 49 ) cm²
= 294 cm²

Lateral surface area of the cube = 4 * (Side)²
= ( 4 * 7² ) cm²
= (4 * 49 ) cm²
= 196 cm²

Hence, the total surface area of the cube is 294 cm² and its lateral surface area is 196 cm².
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Q.5)Water is poured in a cuboidal reservoir at the rate of 60 liters per minute. If the volume of the reservoir is 108m³, find the number of hours it will take to fill the reservoir.

SOLUTION:

Given:
We know that 1m³ = 1,000L
Quantity of water in the reservoir = 108 * 1,000 = 1,08,000 liters

Rate of pouring water = 60 liters per minute
Volume of water filled in 1 minute = 60 L
Volume of water filled in 1 hour = 60 * 60 L = 3,600 L

Now 3,600 L water is filed in 1 hour

1 L water be filled in 1 / 3600 hours

1,08,000 L water will be filled in 1 , 3600 * 1,08,000 = 30 hours

Hence, the reservoir will be filled in 30 hours.
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