What is the mass of water required to fill a circular hot tub 3.6 m in diameter and 1.3 m deep? Answer in units of kg.
Convert 3.6 m to cm and 1.3 m to cm.
volume = (pi*dia/4)
density = 1.00 g/cc
mass = volume x density = grams
Convert to kg.
To find the mass of water required to fill the circular hot tub, we need to calculate the volume of water first and then multiply it by the density of water.
Step 1: Calculate the volume of water.
The hot tub is shaped like a cylinder, so we can use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height (or depth) of the tub.
Given:
Diameter = 3.6 m
Radius (r) = Diameter / 2 = 3.6 m / 2 = 1.8 m
Height (h) = 1.3 m
Using the values, we can calculate the volume:
V = π × (1.8 m)^2 × 1.3 m
Step 2: Convert the volume to mass.
The density of water is approximately 1000 kg/m^3. Therefore, to find the mass, we can multiply the volume by the density:
Mass = Volume × Density
= V × 1000 kg/m^3
Now, let's calculate the mass of water required to fill the hot tub:
Mass = (π × (1.8 m)^2 × 1.3 m) × 1000 kg/m^3