A swimming pool is in the shape of a cuboid with dimensions 50 metres long by 25 metros wide by 2.5 metres deep. If the pool is completely filled with water, calculate
a) the volume of water in the pool
b) the longest straight distance a swimmer could swim in the pool
c0 the angle the straight path in (b) makes the end of the pool.
My answers are for a) 3125 cm ^3
b)55.9 m
c) 45 degrees.
Please is it correct?
Thak you so much
Have a great day
Lucas
a: wrong units. 3125 m^3
b: ok
c: tanθ = 50/25
that's not 45°
consider the diagonal of the rectangular bottom and the end of the pool. The z-axis does not matter.
Steve, thank you so much, you are amazing!!!!!
To calculate the answers, you need to use the formulas for volume, distance, and angle. Let's go through them step by step.
a) Volume of water in the pool:
To find the volume of a cuboid (rectangular prism), you multiply its length (L), width (W), and height (H). In this case, the length is 50 m, the width is 25 m, and the depth is 2.5 m. So, the volume is:
Volume = L * W * H
= 50 m * 25 m * 2.5 m
= 3125 cubic meters
So, the volume of water in the pool is 3125 cubic meters. It's important to note that the answer should be in cubic meters, not cubic centimeters.
b) Longest straight distance a swimmer could swim:
The longest straight distance a swimmer could swim in the pool is the diagonal of the cuboid. To calculate this, we can use the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, we consider the length (L), width (W), and depth (H) of the pool as the sides of a right triangle. So, the longest distance (D) can be calculated as:
D = √(L^2 + W^2 + H^2)
= √(50^2 + 25^2 + 2.5^2)
≈ 55.9 m
Therefore, the longest straight distance a swimmer could swim in the pool is approximately 55.9 meters.
c) Angle the straight path makes with the end of the pool:
To find the angle, we can use trigonometry. We can consider the longer side (L) and the height (H) as the sides of a right triangle. The angle (θ) can be calculated using the inverse tangent function:
θ = arctan(L / H)
= arctan(50 m / 2.5 m)
≈ 80.54 degrees
So, the angle the straight path makes with the end of the pool is approximately 80.54 degrees. Please note that this angle will correspond to the angle between the longest side and the vertical direction.
Your answers:
a) 3125 cubic meters (not cm^3)
b) approximately 55.9 meters
c) approximately 80.54 degrees (not 45 degrees)
I hope this clarifies the calculations for you! If you have any further questions, please feel free to ask.