Solid Mensuration Practice Problems :
Here we are going to see an example problem on the topic mensuration.
Question 1 :
The barrel of a fountain-pen cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used for writing 330 words on an average. How many words can be written using a bottle of ink containing one fifth of a litre?
To find the number of words can be written using a bottle of inck, we have to find the quantity of ink in the barrel.
Volume of barrel in the cylindrical shape = πr2h
height of shape = 7 cm
radius of the shape = (5/2) mm
10 mm = 1 cm
(5/2)/10 = (1/4) cm
Volume of barrel in the cylindrical shape :
= (22/7) ⋅ (1/4) (1/4) 7
= (11/8) cm3
1000 cm3 = 1 liter
= 11/8000 liter
Quantity of ink in 1 liter = 8000/11
Quantity of ink in the bottel = (1/5) of liter of ink in the barrel
= (1/5) (8000/11)
Number of word written using 1 bottel of ink = 330
Required number of words = (1/5) (8000/11) ⋅ (1/4)
= 48000 words
Question 2 :
A hemi-spherical tank of radius 1.75 m is full of water. It is connected with a pipe which empties the tank at the rate of 7 litre per second. How much time will it take to empty the tank completely?
To solve this problem, first let us find quantity of water in the tank in liters.
Volume of water in the hemispherical tank = (2/3)πr3
= (2/3) ⋅ (22/7) ⋅ (1.75)3
= (2/3) ⋅ (22/7) (1.75) (1.75) (1.75)
= 11.22 m3
1 m3 = 1000 liter
= 11.22 (1000)
= 11220 liters
Quantity of water empties = 7 liter per second
= 7 (60)
= 420 liter per minute
Time taken to empty the tank = 11220/420
= 27 minutes (approximately)
Question 3 :
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r units.
Volume of cone craved out from the hemisphere
= (1/3) r2h
= (1/3) r2r
= (1/3) r3
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