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Calculate the area and cost of carpeting a square room, the area of a square farmyard, and the volume of a cube-shaped box.

Mathematics

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here are the answers and explanations for these problems:

1. a) Mrs Lehola's bedroom carpet:

  1. Calculate the area of the square room.

    The length of the room is 5 m5 \text{ m}.
    The formula for the area of a square is Area=length2\text{Area} = \text{length}^2.

    Area=(5 m)2=25 m2\text{Area} = (5 \text{ m})^2 = 25 \text{ m}^2
  2. Calculate the total cost of the carpeting.

    The cost is R70\text{R}70 per m2\text{m}^2.

    Total Cost=25 m2×R70/m2=R1750\text{Total Cost} = 25 \text{ m}^2 \times \text{R}70/\text{m}^2 = \text{R}1750

    Mrs Lehola needs to buy 25 m2\boxed{25 \text{ m}^2} of carpeting, and it will cost R1750\boxed{\text{R}1750}.

    1. b) Mrs Lehola's farmyard:

  3. Calculate the area of the farmyard.

    The farmyard is 600 m600 \text{ m} long and 600 m600 \text{ m} wide.
    The formula for the area of a rectangle (or square) is Area=length×width\text{Area} = \text{length} \times \text{width}.

    Area=600 m×600 m=360000 m2\text{Area} = 600 \text{ m} \times 600 \text{ m} = 360000 \text{ m}^2

    The area of her farm is 360000 m2\boxed{360000 \text{ m}^2}.

    2. a) Volume of the box of biscuits:

  4. Calculate the volume of the box.

    The box has a length of 10 cm10 \text{ cm}, a breadth of 10 cm10 \text{ cm}, and a height of 10 cm10 \text{ cm}.
    The formula for the volume of a rectangular prism is Volume=length×breadth×height\text{Volume} = \text{length} \times \text{breadth} \times \text{height}.

    Volume=10 cm×10 cm×10 cm=1000 cm3\text{Volume} = 10 \text{ cm} \times 10 \text{ cm} \times 10 \text{ cm} = 1000 \text{ cm}^3

    The volume of the box is 1000 cm3\boxed{1000 \text{ cm}^3}.

    2. b) Volume of Mr Radebe's bathroom:

  5. Determine the side length of the cubic bathroom.

    A cubic bathroom has equal length, breadth, and height. The height is given as 3 m3 \text{ m}, so the length and breadth are also 3 m3 \text{ m}.

  6. Calculate the volume of the bathroom.

    The formula for the volume of a cube is Volume=side3\text{Volume} = \text{side}^3.

    Volume=(3 m)3=3 m×3 m×3 m=27 m3\text{Volume} = (3 \text{ m})^3 = 3 \text{ m} \times 3 \text{ m} \times 3 \text{ m} = 27 \text{ m}^3

    The volume of his bathroom is 27 m3\boxed{27 \text{ m}^3}.

    2. c) Length of the side of the toy dice:

  7. Find the cube root of the volume.

    The volume of the dice is 216 cm3216 \text{ cm}^3. Since it's a cube, its volume is side3\text{side}^3.
    We need to find the side length, so we take the cube root of the volume.

    side3=216 cm3\text{side}^3 = 216 \text{ cm}^3 side=216 cm33\text{side} = \sqrt[3]{216 \text{ cm}^3} side=6 cm\text{side} = 6 \text{ cm}

    The length of the side of the dice is 6 cm\boxed{6 \text{ cm}}.

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