A manufacturer drills a round hole of radius r through the center of a metal sphere of radius r. find the volume of the remainin
g metal “bead.”
1 answer:
The media attached below is the bottom/top view of drilled sphere. If you look it from sideways, you'll see that the drilled hole is in the form of cylindrical shape. So,
Volume of the drilled shape= volume of cylinder = πr²h, where h is 2r.
∴Volume of cylinder(V1) = πr²(2r) = 2πr³.
Volume of sphere(V2) = 4πr³/3.
Therefore volume of remaining metal bead = V1 - V2
= 2πr³ - 4πr³/3
= (6πr³ - 4πr³)/3
= 2πr³/3.
Hence volume of remaining bead is 2πr³/3
Volume of the drilled shape= volume of cylinder = πr²h, where h is 2r.
∴Volume of cylinder(V1) = πr²(2r) = 2πr³.
Volume of sphere(V2) = 4πr³/3.
Therefore volume of remaining metal bead = V1 - V2
= 2πr³ - 4πr³/3
= (6πr³ - 4πr³)/3
= 2πr³/3.
Hence volume of remaining bead is 2πr³/3
You might be interested in
The volume prism refers to the number of cubic units that will exactly fill the figure. The volume of a rectangular prism can be found or calculate by using the formula V=Bh, where B represents to the area of the base or in other words the length and width of the rectangle.
In this exercise is given that the measurements of a prism are 5/2ft, 3/2ft, and 7/2ft; and it is asked to find its volume. In order to find the volume of the prism, you should substitute the given values into the previous mention formula.
V=Bh
V=(5/2 ft)(7/2 ft)(3/2 ft)
V=(35/4 ft²)(3/2 ft)
V=105/8ft³ or
ft³
The volume of the rectangular prism isft³.
In this exercise is given that the measurements of a prism are 5/2ft, 3/2ft, and 7/2ft; and it is asked to find its volume. In order to find the volume of the prism, you should substitute the given values into the previous mention formula.
V=Bh
V=(5/2 ft)(7/2 ft)(3/2 ft)
V=(35/4 ft²)(3/2 ft)
V=105/8ft³ or
The volume of the rectangular prism is