Hello ma’am sir.. I have a problem in my assignment.. I‘m now a college student…a first year student…this is my question..please help me.. I really need it now… 1. The diameter of the earth is 7920 miles, and that of the moon is 2160 miles. Compare their volumes.
2. A pyramid V-ABCD is cut from a cube of edge 12 inch. The vertex V is the midpoint of an upper edge of the cube. Compute the lateral surface of the pyramid.
In my book.. There’s an answer given..but there’s no solution..
The answer of number one is>>> V of earth=(198)cube over the V of moon=(54)cube…
And for the number two is>>> 334.82 sq.in.
V = 4/3πr^3
Have you compared the two volumes?
I'm not sure what the second question is asking.
I hope this helps a little.
volume is proportional to length dimension cubed for similar shapes.
V2/V1 = (D2/D1)^3
Hello! I'll be happy to help you with your assignment questions.
1. To compare the volumes of the Earth and the Moon, you need to use the formula for the volume of a sphere: V = (4/3) * π * r^3. However, since you are given the diameters of the Earth and the Moon, you first need to find their radii.
- Radius of the Earth: Divide the diameter by 2. So, the radius of the Earth is 7920 miles / 2 = 3960 miles.
- Radius of the Moon: Divide the diameter by 2. So, the radius of the Moon is 2160 miles / 2 = 1080 miles.
Now, you can calculate their volumes using the formula mentioned earlier:
- Volume of the Earth: V_earth = (4/3) * π * (3960 miles)^3
- Volume of the Moon: V_moon = (4/3) * π * (1080 miles)^3
To compare the volumes, divide the volume of the Earth by the volume of the Moon:
V_earth / V_moon = [(4/3) * π * (3960 miles)^3] / [(4/3) * π * (1080 miles)^3]
Simplifying the expression, we get: (3960 miles / 1080 miles)^3
And finally, calculate the numerical value of the ratio to compare their volumes.
2. To compute the lateral surface area of the pyramid, we need to know the slant height of the pyramid. Unfortunately, the information you provided does not include the slant height of the pyramid. Without that information, it is not possible to derive the solution.
I suggest checking your textbook or assignment instructions again to see if there is any missing information or formula that can help you find the slant height.