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A diagram shows a swimming pool divided into a shallow end and a deep end. Calculate the area of each section and the total pool area. Also, determine the volume of the deep end.

Mathematics

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Answers

4 parts
a

3 m2\text{3 m}^2

b

20 m2\text{20 m}^2

c

23 m2\text{23 m}^2

d

40 m3\text{40 m}^3

Step-by-step solution

9 steps

Here are the calculations based on the provided diagram:

Part a· 2 steps

Area of the Shallow end

  1. Identify the dimensions of the shallow end.

    The shallow end is a rectangle with a length of 3 m3 \text{ m} and a width of 1 m1 \text{ m}.

  2. Calculate the area using the formula for a rectangle, A=length×widthA = \text{length} \times \text{width}.

    Ashallow=3 m×1 m=3 m2A_{\text{shallow}} = 3 \text{ m} \times 1 \text{ m} = \boxed{\text{3 m}^2}

Part b

20 m2\text{20 m}^2

Area of the Deep end

  1. Identify the dimensions of the deep end.

    The deep end is a rectangle with a length of 5 m5 \text{ m} and a width of 4 m4 \text{ m}.

  2. Calculate the area using the formula for a rectangle, A=length×widthA = \text{length} \times \text{width}.

    Adeep=5 m×4 m=20 m2A_{\text{deep}} = 5 \text{ m} \times 4 \text{ m} = \boxed{\text{20 m}^2}

Part c

23 m2\text{23 m}^2

Area of the pool

  1. Sum the areas of the shallow and deep ends to find the total area of the pool.

    Apool=Ashallow+AdeepA_{\text{pool}} = A_{\text{shallow}} + A_{\text{deep}}

  2. Substitute the calculated values and find the total area.

    Apool=3 m2+20 m2=23 m2A_{\text{pool}} = 3 \text{ m}^2 + 20 \text{ m}^2 = \boxed{\text{23 m}^2}

Part d

40 m3\text{40 m}^3

Volume at deep end

  1. Identify the dimensions and depth of the deep end.

    The deep end has a length of 5 m5 \text{ m}, a width of 4 m4 \text{ m}, and a depth of 2 m2 \text{ m}.

  2. Calculate the volume using the formula V=length×width×depthV = \text{length} \times \text{width} \times \text{depth}.

    Vdeep=5 m×4 m×2 mV_{\text{deep}} = 5 \text{ m} \times 4 \text{ m} \times 2 \text{ m}

  3. Perform the multiplication.

    Vdeep=20 m2×2 m=40 m3V_{\text{deep}} = 20 \text{ m}^2 \times 2 \text{ m} = \boxed{\text{40 m}^3}
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