To find volume of the shapes, we will be using the formulas given below.
Volume of sphere = (4/3) π r^{3}
Volume of hemisphere = (2/3) π r^{3}
Volume of cone = (1/3) π r^{2}h
Volume of cylinder = π r^{2}h
Problem 1 :
A steel bar is 2.2 m long and has a diameter of 5 cm. Find the volume of the bar in cm^{3}.
Solution :
Length of steel bar = 2.2 m (or) 220 cm
Radius = 5/2 ==> 2.5 cm
Volume of steel bar = π r^{2}h
= (3.14) (2.5)^{2}(220)
= 4317.5 cm^{3}
Problem 2 :
A stainless steel wine vat is cylindrical with base diameter 1.8 m and height 6 m. How much wine does it hold if it is 90% full?
Solution :
Radius = 1.8 m, height = 6 m
Volume of steel bar = 90% of π r^{2}h
= 0.90 x 3.14 x (1.8)^{2} x 6
= 54.93 m^{3}
Problem 3 :
A box has a square base and its height is 12 cm. If the volume of the box is 867 cm^{3}, find its length.
Solution :
Let base length of the square as x.
Volume of box = 867 cm^{3}
Area of square base x height = 867
x^{2} x 12 = 867
x^{2} = 867/12
x^{2} = 72.25
x = 8.5 cm
Problem 4 :
15.4 mm of a rain falls on a rectangular shed roof of length 12 m and width 5.5 m. All of the water goes into a cylindrical tank of base diameter 4.35 m. By how much does the water level in the tank rise in mm ?
Solution :
Measures of rectangular shed :
Length = 12 m = 12000 mm
width = 5.5 m = 5500 mm
height = 15.4 mm
Radius = 4.35/2 = 2.175 m
= 2175 mm
Volume of water in rectangular tank = Volume of water in cylindrical tank
length x width x height = π r^{2}h
12000 x 5500 x 15.4 = 3.14 x (2.175)^{2} x h
h = (12000 x 5500 x 15.4)/3.14 x (2175)^{2}
h = 68.42 mm
Problem 5 :
Find the volume of the figure shown below.
Solution :
Volume = Base area x height
Base area = Area of large circle - Area of small circle
Let R and r be radius of large and small circles respectively.
R = 0.8/2, r = 0.4/2
R = 0.4 m and r = 0.2 m
Area of base = πR^{2} - πr^{2}
= π(0.4^{2} - 0.2^{2})
= 3.14(0.12)
Area of base = 0.3768 m^{2}
Height = 1.2 m
Volume = 0.3768 x 1.2
= 0.45216 m^{3}
Problem 6 :
Find the volume of the figure given below.
Solution :
Volume of cylinder = πr^{2}h
radius = 6 cm and height = 10 cm
= π(6)^{2 }(10)
= 3.14(36)(10)
Volume of cylinder = 1130.4 cm^{3}
Problem 7 :
Tom has just had a load of sand delivered. A pile of sand is in the shape of a cone of radius 1.6 m and height 1.2 m. Find the volume of sand Tom has had delivered.
Solution :
Volume of sand to be delivered = (1/3) πr^{2}h
radius = 1.6 m and height = 1.2 m
= (1/3) π(1.6)^{2}(1.2)
= (1/3)x3.14x(1.6)^{2}(1.2)
= 3.19 m^{3}
Volume of sand delivered is 3.19 m^{3}_{.}
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