A swimming pool measures 50.0 meters by 25.0 meters. How many grams of water are needed to fill the pool, whose average depth is 7.8 feet? Assume the density of water to be 1.0 g/mL.

Question

Wyatt Atkins · Accepted Answer

The mass of water needed is #3.0 × 10^9color(white)(l) "g"#.

The formula for density is #color(blue)(|bar(ul(color(white)(a/a) "Density" = "Mass"/"Volume" color(white)(a/a)|)))" "# or #color(blue)(|bar(ul(color(white)(a/a) ρ = m/Vcolor(white)(a/a)|)))" "# And the formula for volume is #color(blue)(|bar(ul(color(white)(a/a) "Volume" = "length" × "width" × "height"color(white)(a/a)|)))" "# or #color(blue)(|bar(ul(color(white)(a/a) V = lwh color(white)(a/a)|)))" "# Step 1. Convert the depth of the pool from feet to metres. #h = 7.8 color(red)(cancel(color(black)("ft"))) × (12 color(red)(cancel(color(black)("in"))))/(1 color(red)(cancel(color(black)("ft")))) × "1 m"/(39.37 color(red)(cancel(color(black)("in")))) = 2.38 "m"# Step 2. Calculate the volume of the water # V = lwh = "50.0 m× 25.0 m × 2.38 m" = 2980color(white)(l) "m"^3# Step 3. Convert the volume of the water to millilitres. The density of water is given as 1.0 g/mL, so we should convert the volume to millilitres. #V = 2980 color(red)(cancel(color(black)("m"^3))) ×( 1000 color(red)(cancel(color(black)("L"))))/(1 color(red)(cancel(color(black)("m"^3)))) × "1000 mL"/(1 color(red)(cancel(color(black)("L")))) = 2.98 × 10^9color(white)(l) "mL"# Step 4. Calculate the mass of the water. Since #ρ = m/V, m = ρ V# ∴ #m = "1.0 g"/(1 color(red)(cancel(color(black)("mL")))) × 2.98 × 10^9 "mL" = 3.0 × 10^9color(white)(l) "g"#

Axel Alvarado · Answer

undefined To find the volume of water needed to fill the pool, we first need to convert the dimensions of the pool to meters. Since 1 foot is approximately 0.3048 meters, the depth of the pool in meters is 7.8 feet * 0.3048 meters/foot = 2.37744 meters.

The volume of water needed to fill the pool is then calculated by multiplying the length, width, and depth of the pool:

Volume = Length * Width * Depth
Volume = 50.0 meters * 25.0 meters * 2.37744 meters = 5943.6 cubic meters

Since the density of water is 1.0 g/mL, we can convert the volume of water from cubic meters to grams:

1 cubic meter of water = 1000 liters = 1000 kg = 1,000,000 grams

So, 5943.6 cubic meters * 1,000,000 grams/cubic meter = 5,943,600 grams of water are needed to fill the pool.

Peyton Adams · Answer

undefined First, convert the dimensions of the swimming pool to meters, as the density of water is given in grams per milliliter.

1 foot = 0.3048 meters (approximately)
So, the average depth of the pool in meters is:
7.8 feet * 0.3048 meters/foot = 2.37744 meters

Now, calculate the volume of water needed to fill the pool:
Volume = Length * Width * Depth
Volume = 50.0 meters * 25.0 meters * 2.37744 meters

Since density = mass / volume, rearrange the equation to solve for mass:
mass = density * volume

Substitute the given density of water (1.0 g/mL) and the calculated volume into the equation to find the mass in grams.