Here are the solutions to the questions:
7.1 If the 300 cm side of the rectangular tin plate is bent to form a circle, determine the diameter of the cylindrical tank. You may use the formula: Circumference of a circle = π× diameter; Using π=3.14.
Step 1: Identify the circumference of the circle.
When the 300 cm side of the rectangular tin plate is bent to form a circle, this length becomes the circumference (C) of the circle.
C=300 cm
Step 2: Use the given formula for the circumference of a circle.
C=π×D
Where D is the diameter and π=3.14.
Step 3: Substitute the values and solve for the diameter (D).
300cm=3.14×D
D=3.14300cm
D≈95.5414 cm
Rounding to two decimal places:
D≈95.54 cm
The diameter of the cylindrical tank is 95.54cm.
7.2 Calculate the volume of water that the cylindrical tank can hold in litres. You may use the formula: Volume of a cylindrical tank = π×r2× height; Using π=3.14 and 1000cm3=1 litre.
Step 1: Determine the radius (r) and height (h) of the cylindrical tank.
From 7.1, the diameter (D) is approximately 95.5414 cm.
The radius (r) is half of the diameter:
r=2D=295.5414cm=47.7707 cm
The height (h) of the cylindrical tank is the other dimension of the rectangular plate:
h=250 cm
Step 2: Calculate the volume of the cylindrical tank using the formula V=πr2h.
Using π=3.14:
V=3.14×(47.7707cm)2×250 cm
V=3.14×2282.038cm2×250 cm
V=3.14×570509.5cm3
V≈1791799.83cm3
Step 3: Convert the volume from cubic centimeters to litres.
Given 1000cm3=1 litre.
Vlitres=1000cm3/litre1791799.83cm3
Vlitres≈1791.79983 litres
Rounding to the nearest litre:
Vlitres≈1792 litres
The volume of water the cylindrical tank can hold is approximately 1792litres.
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