Question

The bathysphere was an early version of a submarine, invented in the 1930s. The inside

diameter of the bathysphere was 56 inches, and the steel used to make the sphere was 1.5
inches thick. It had three 10-inch diameter windows. Estimate the volume of steel used to
make the bathysphere to the nearest whole number.
It took about
in.of steel to make the bathysphere.

Answer 1

The volume of steel used to make the bathysphere is approximately 53,481 cubic inches.

Step-by-step explanation:

To estimate the volume of steel used to make the bathysphere, we need to calculate the volume of the sphere and subtract the volume of the windows. The volume of the sphere can be calculated using the formula for the volume of a sphere: V = (4/3)πr³, where r is the radius of the sphere. Since the diameter of the bathysphere is 56 inches, the radius is half of that, which is 28 inches. Converting to meters, the radius is approximately 0.7112 meters.

Now we can calculate the volume of the sphere: V = (4/3)π(0.7112)³ ≈ 0.8827 cubic meters.

The volume of each window can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius of the window and h is the height of the window. The radius of each window is half of the diameter, which is 5 inches or approximately 0.127 meters. The height of each window is 1.5 inches or approximately 0.0381 meters.

Now we can calculate the volume of each window: V = π(0.127)²(0.0381) ≈ 0.0024 cubic meters.

Since there are three windows, the total volume of the windows is 3 × 0.0024 ≈ 0.0073 cubic meters.

To estimate the volume of steel used to make the bathysphere, we subtract the volume of the windows from the volume of the sphere: approximately 0.8827 - 0.0073 ≈ 0.8754 cubic meters.

Finally, we convert the volume to cubic inches to estimate the amount of steel used: 0.8754 × 61023.7 ≈ 53481 cubic inches. Rounding to the nearest whole number, the volume of steel used to make the bathysphere is approximately 53,481 cubic inches.

Answer 2

Step-by-step explanation:

The shape of bathysphere submarine is a sphere and can be imagined as concentric sphere.

Given inside diameter of bathysphere = 56in or radius will be
`(56)/(2)` inch

Volume of inside sphere =
`(4)/(3) \pi r^(3)` =
`(4)/(3)\pi 28^(3)`

Since the steel is 1.5 inch thick, the volume of outside sphere =
`(4)/(3) \pi r^(3)`

The changed r will
`(4)/(3) \pi r^(3)` =
`(4)/(3)\pi (57.5)/(2)^(3)`

Volume of steel =
`(4)/(3)\pi 28.75^(3) -(4)/(3)\pi 28^(3)` =
`(4)/(3)\pi (28.75^(3) -28^(3))`