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1.5 A basic geometrical shape with a circular base. 1.2.1 What kind of three-dimensional shape does the tank represent?
Mathematics
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6 stepsHere is the solution to Question 1:
1.1 Matching
- 1.1.1 A basic shape with three angles and three sides. D Triangle
- 1.1.2 A line segment from the centre of the circle to the circle boundary. F Radius
- 1.1.3 A device that measures temperature. A Thermometer
- 1.1.4 The distance around the 2-dimensional shape. B Perimeter
- 1.1.5 A basic geometrical shape with a circular base. C Cylinder
1.2 Water Tank Calculations
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1.2.1 What kind of three-dimensional shape does the tank represent? The tank represents a Cylinder.
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1.2.2 Calculate the radius of the water tank.
Identify the given diameter.
The diameter $D = 2.4 \text{ M}$.Calculate the radius using the formula .
$$ r = \frac{2.4 \text{ M}}{2} $$ $$ r = \boxed{\text{1.2 M}} $$- 1.2.3 Calculate the circumference of the tank.
Use the radius calculated in 1.2.2 and the given value for .
Given $r = 1.2 \text{ M}$ and $\pi = 3.14$.Apply the formula for circumference .
$$ C = 2 \times 3.14 \times 1.2 \text{ M} $$ $$ C = 6.28 \times 1.2 \text{ M} $$ $$ C = \boxed{\text{7.536 M}} $$- 1.2.4 Calculate the volume of water in m that the tank can hold if the radius of the dam is 2m and the height is 300cm.
Identify the given dimensions and convert units if necessary.
Given radius $r = 2 \text{ m}$. Given height $h = 300 \text{ cm}$. Convert height to meters: $$ h = 300 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 3 \text{ m} $$ Use $\pi = 3.14$.Apply the formula for the volume of a cylinder .
$$ V = 3.14 \times (2 \text{ m})^2 \times 3 \text{ m} $$ $$ V = 3.14 \times 4 \text{ m}^2 \times 3 \text{ m} $$ $$ V = 3.14 \times 12 \text{ m}^3 $$ $$ V = \boxed{\text{37.68 m}^3} $$
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