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Please help me get the calculation of the netball court with L=36m W=18m H=9m

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4 parts
a

648 m2\text{648 m}^2

b

108 m\text{108 m}

c

5832 m3\text{5832 m}^3

d

2268 m2\text{2268 m}^2

Step-by-step solution

11 steps

You've provided the dimensions of a netball court: Length (L) = 36m, Width (W) = 18m, and Height (H) = 9m. You've also listed some formulas. I will calculate the area of the court, its perimeter, the volume of the space above it, and the surface area of a rectangular prism with these dimensions.

Part a· 2 steps

Area of the court

  1. Use the formula for the area of a rectangle, A=L×WA = L \times W.

    A=36 m×18 mA = 36\, \text{m} \times 18\, \text{m}

  2. Calculate the area.

    A=648 m2A = 648\, \text{m}^2

    The area of the netball court is 648 m2\boxed{\text{648 m}^2}.

Part b

108 m\text{108 m}

Perimeter of the court

  1. Use the formula for the perimeter of a rectangle, P=2(L+W)P = 2(L + W).

    P=2(36 m+18 m)P = 2(36\, \text{m} + 18\, \text{m})

  2. Calculate the sum of length and width.

    P=2(54 m)P = 2(54\, \text{m})

  3. Calculate the perimeter.

    P=108 mP = 108\, \text{m}

    The perimeter of the netball court is 108 m\boxed{\text{108 m}}.

Part c

5832 m3\text{5832 m}^3

Volume of the space above the court

  1. Use the formula for the volume of a rectangular prism, V=L×W×HV = L \times W \times H.

    V=36 m×18 m×9 mV = 36\, \text{m} \times 18\, \text{m} \times 9\, \text{m}

  2. Calculate the volume.

    V=648 m2×9 mV = 648\, \text{m}^2 \times 9\, \text{m} V=5832 m3V = 5832\, \text{m}^3

    The volume of the space above the court is 5832 m3\boxed{\text{5832 m}^3}.

Part d

2268 m2\text{2268 m}^2

Surface area of a rectangular prism with these dimensions

  1. Use the formula for the surface area of a rectangular prism, SA=2(LW+LH+WH)SA = 2(LW + LH + WH).

    SA=2((36 m×18 m)+(36 m×9 m)+(18 m×9 m))SA = 2((36\, \text{m} \times 18\, \text{m}) + (36\, \text{m} \times 9\, \text{m}) + (18\, \text{m} \times 9\, \text{m}))

  2. Calculate each product.

    SA=2(648 m2+324 m2+162 m2)SA = 2(648\, \text{m}^2 + 324\, \text{m}^2 + 162\, \text{m}^2)

  3. Sum the areas.

    SA=2(1134 m2)SA = 2(1134\, \text{m}^2)

  4. Calculate the total surface area.

    SA=2268 m2SA = 2268\, \text{m}^2

    The surface area of a rectangular prism with these dimensions is 2268 m2\boxed{\text{2268 m}^2}.

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