A right pyramid on a base 10cm square is 15m high .find the volume of the pyramid.if the top 6m of the pyramid are removed,what is the volume of the remaining frustum.
first off, do you mean the base is
"10 cm square" = 10 by 10 or 100cm^2
or just "10 cm squared" = 10 cm^2
?? In any case
V = 1/3 Bh
if the top 6m are removed, that is a similar pyramid of 2/5 scale, so its volume is 8/125 B. so subtract that from the original volume.
or use the handy formula derived at
en.wikipedia.org/wiki/Frustum
To find the volume of the right pyramid, we can use the formula:
Volume = (1/3) * base area * height.
Given that the base is a square with side length 10 cm, the base area would be (10 cm)^2 = 100 cm^2.
The height of the pyramid is given as 15 m. However, since the base area is in square centimeters and the height is in meters, we need to convert the height to centimeters:
15 m = 15 * 100 cm = 1500 cm.
Now we can calculate the volume of the pyramid:
Volume = (1/3) * 100 cm^2 * 1500 cm
= 50000 cm^3.
To find the volume of the remaining frustum, we need to subtract the volume of the top portion that was removed from the original pyramid.
The top portion that was removed has a height of 6 m. Converting to centimeters:
6 m = 6 * 100 cm = 600 cm.
To find the volume of the removed portion, we can also use the formula for the volume of a pyramid and subtract it from the volume of the original pyramid:
Volume of removed portion = (1/3) * 100 cm^2 * 600 cm
= 20000 cm^3.
Finally, we can find the volume of the remaining frustum:
Volume of frustum = Volume of original pyramid - Volume of removed portion
= 50000 cm^3 - 20000 cm^3
= 30000 cm^3.
To find the volume of the right pyramid, we can use the formula:
Volume = (1/3) * Base Area * Height
In this case, the base area is a square with sides of 10 cm, so the area is 10 cm * 10 cm = 100 cm^2.
The height given is 15 m, but since the base area is in cm^2, we need to convert the height to centimeters. There are 100 cm in 1 m, so the height is 15 m * 100 cm/m = 1500 cm.
Using the formula, the volume of the pyramid is:
Volume = (1/3) * 100 cm^2 * 1500 cm = 50,000 cm^3.
Now, if the top 6 m (600 cm) of the pyramid is removed, we are left with a frustum (truncated pyramid). The remaining height of the frustum is 1500 cm - 600 cm = 900 cm.
To find the volume of the frustum, we can use the formula:
Volume of Frustum = (1/3) * Height * (Base Area1 + Base Area2 + √(Base Area1 * Base Area2))
The base area of the larger base of the frustum (after removing the top) is still 100 cm^2.
To find the base area of the smaller top base, we need to calculate the area of a square with sides of 10 cm minus the area of a square with sides of 6 cm (the portion that was removed).
Area of smaller top base = 10 cm * 10 cm - 6 cm * 6 cm = 100 cm^2 - 36 cm^2 = 64 cm^2.
Using the formula, the volume of the frustum is:
Volume of Frustum = (1/3) * 900 cm * (100 cm^2 + 64 cm^2 + √(100 cm^2 * 64 cm^2))
Volume of Frustum = (1/3) * 900 cm * (164 cm^2 + √(6400 cm^2))
Volume of Frustum = (1/3) * 900 cm * (164 cm^2 + 80 cm)
Volume of Frustum = (1/3) * 900 cm * 244 cm^2
Volume of Frustum = 70,200 cm^3
Therefore, the volume of the remaining frustum is 70,200 cm^3.
Please check for typos. Do you really mean a 15 meter high structure on a 100 square CENTIMETER base?
In general the volume of a pointy object with straight sides is 1/3 the area of the base times the height.
Same for the top 6 meters so find it and subtract it.