A solid is composed of a cube with side length 6 meters and a hemisphere with diameter 6 meters. Find the volume of the solid.
272.55
300.82
Well, isn't that a solid puzzle! Let's break it down, shall we?
The volume of a cube is given by the formula: V = s^3, where "s" is the side length. So, the volume of the cube is 6^3 = 216 cubic meters.
Now, let's talk about that hemisphere. The formula for the volume of a hemisphere is: V = (2/3) * π * r^3, where "r" is the radius. In this case, the diameter is 6 meters, so the radius is half of that, which is 3 meters. Plugging that into the formula, we get V = (2/3) * π * 3^3.
Now comes the fun part – adding the two volumes together! So, the total volume of the solid is 216 cubic meters + (2/3) * π * 3^3 cubic meters.
I'm sure you can do the math from here, but if you need help, I'm here to lend a hand (or a clown nose, as the case may be)!
To find the volume of the solid, we need to find the volume of the cube and the volume of the hemisphere, and then add them together.
1. Volume of the Cube:
The volume of a cube is calculated by multiplying the length, width, and height. Since all sides of the cube have a length of 6 meters, the volume is given by:
Volume of Cube = side length ^ 3 = 6^3 = 216 cubic meters.
2. Volume of the Hemisphere:
The volume of a hemisphere is given by the formula (2/3)πr^3, where r is the radius of the hemisphere. In this case, the radius is half of the diameter, so it is 6 / 2 = 3 meters.
Volume of Hemisphere = (2/3) * π * 3^3 = (2/3) * π * 27 = 18π cubic meters.
3. Calculate the Total Volume:
To find the volume of the solid, we add the volumes of the cube and hemisphere together:
Total Volume = Volume of Cube + Volume of Hemisphere
= 216 cubic meters + 18π cubic meters
So, the volume of the solid is 216 cubic meters + 18π cubic meters, or approximately 261.59 cubic meters.
I'm sorry, I cannot determine the context of these numbers without additional information or a question. Can you please provide more context so that I can assist you better?
A solid
V of cube = side*side*side = 6*6*6 = 216
V of hemisphere = 1/2 of V of sphere = 4/3*pi*radius cubed = 1/2(4/3(pi 3cubed))= 1/2(4/3(pi 27)= 1/2(36pi)= [18pi meters] or [56.52 meters]