find the volume of a regular pentagonal pyramid whose sides measure 12m and height is 15m.
the area of the base is 1/2 apothem*perimeter
v = 1/3 Bh
Cylinder A has a volume of 360 cm2. Cylinder B has a base and height identical to that of Cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of Cylinder B?
To find the volume of a regular pentagonal pyramid, you can use the formula:
Volume = (1/3) * Base Area * Height
First, let's find the base area of the pentagonal pyramid. Since the pyramid is regular, we know that all the sides are equal in length. The side length of the pentagon is given as 12m.
To find the base area, we need to determine the apothem (the distance from the center of the pentagon to any of its sides) and the perimeter of the pentagon.
Since the pentagon is regular, we can use the formula:
Apothem = (Side Length) / (2 * tan(180° / Number of Sides))
In this case, the number of sides is 5.
Apothem = 12m / (2 * tan(180° / 5))
Apothem = 12m / (2 * tan(36°))
Using a calculator, we find that tan(36°) ≈ 0.726543, so:
Apothem = 12m / (2 * 0.726543)
Apothem ≈ 8.2775m
Next, let's find the perimeter of the pentagon which is given by:
Perimeter = (Number of Sides) * (Side Length)
Perimeter = 5 * 12m
Perimeter = 60m
Now, we have the apothem (8.2775m) and perimeter (60m) of the pentagon. We can calculate the area of the base using the formula:
Base Area = (Perimeter * Apothem) / 2
Base Area = (60m * 8.2775m) / 2
Base Area = 248.325m²
Now we can use the volume formula to find the volume:
Volume = (1/3) * Base Area * Height
Volume = (1/3) * 248.325m² * 15m
Volume ≈ 1241.625m³ (rounded to three decimal places)
Therefore, the volume of the regular pentagonal pyramid with side length 12m and height 15m is approximately 1241.625 cubic meters.