The question involves matching geometric terms with descriptions, calculating the volume of a rectangular…

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The question involves matching geometric terms with descriptions, calculating the volume of a rectangular prism (water tank), and determining the radius and volume of a cylinder (water bucket).

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1.1 Choose the description in COLUMN B that matches the term in COLUMN A.

1.1.1 Rectangle: B
1.1.2 Perimeter: D
1.1.3 Circumference: F
1.1.4 Circle: E
1.1.5 Square: A

1.2 Calculations for water tank and bucket

1.2.1 Calculate the volume of the water tank.
The water tank is a rectangular prism with length $L = 3.5 \text{ m}$ , breadth $B = 2.5 \text{ m}$ , and height $H = 5.5 \text{ m}$ .

Substitute the given dimensions into the volume formula.
$V = L \times B \times H$ $V = 3.5 \text{ m} \times 2.5 \text{ m} \times 5.5 \text{ m}$
Calculate the volume.
$V = 48.125 \text{ m}^3$
The volume of the water tank is $\boxed{\text{48.125 m}^3}$ .

1.2.2 Determine the radius of the water bucket.
The water bucket has a diameter of $80 \text{ cm}$ .
Calculate the radius by dividing the diameter by 2.
$r = \frac{\text{Diameter}}{2}$ $r = \frac{80 \text{ cm}}{2}$ $r = 40 \text{ cm}$
The radius of the water bucket is $\boxed{\text{40 cm}}$ .

1.2.3 Calculate the volume of the cylindrical bucket in cubic metres.
The water bucket is a cylinder with radius $r = 40 \text{ cm}$ (from 1.2.2) and height $h = 100 \text{ cm}$ . Use $\pi = 3.14$ .
Convert the radius and height to meters.
$r = 40 \text{ cm} = 0.4 \text{ m}$ $h = 100 \text{ cm} = 1 \text{ m}$
Substitute the values into the volume formula for a cylinder.
$V = \pi \times r^2 \times h$ $V = 3.14 \times (0.4 \text{ m})^2 \times 1 \text{ m}$
Calculate the volume.
$V = 3.14 \times 0.16 \text{ m}^2 \times 1 \text{ m}$ $V = 0.5024 \text{ m}^3$
The volume of the cylindrical bucket is $\boxed{\text{0.5024 m}^3}$ .

1.2.4 How many full water buckets are needed to fill the water tank?
Volume of water tank $= 48.125 \text{ m}^3$ (from 1.2.1)
Volume of one water bucket $= 0.5024 \text{ m}^3$ (from 1.2.3)
Divide the volume of the water tank by the volume of one water bucket.
$\text{Number of buckets} = \frac{\text{Volume of water tank}}{\text{Volume of one water bucket}}$ $\text{Number of buckets} = \frac{48.125 \text{ m}^3}{0.5024 \text{ m}^3}$
Calculate the number of buckets and round up to the nearest whole number since only full buckets are used.
$\text{Number of buckets} \approx 95.799$ $\text{Number of buckets} = 96$
96 full water buckets are needed to fill the water tank.

The question involves matching geometric terms with descriptions, calculating the volume of a rectangular prism (water tank), and determining the radius and volume of a cylinder (water bucket).

Step-by-step solution

Substitute the given dimensions into the volume formula.

Calculate the volume.

Calculate the radius by dividing the diameter by 2.

Convert the radius and height to meters.

Substitute the values into the volume formula for a cylinder.

Calculate the volume.

Divide the volume of the water tank by the volume of one water bucket.

Calculate the number of buckets and round up to the nearest whole number since only full buckets are used.

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