The approximate volume of the partial cylinder, considering a sector of 270 degrees with a radius of 4 cm and a height of 10 cm, is approximately 376.8 cubic centimeters.
To find the volume of the partial cylinder, we can use the formula for the volume of a cylinder, considering only the portion enclosed by the sector. The formula for the volume V of a cylinder is V = πr^2h, where r is the radius of the base and h is the height.
In this case, the radius (r) is given as 4 cm, and the height (h) is 10 cm. However, we need to consider only a portion of the cylinder enclosed by a sector of 270 degrees. To account for the fraction of the circle, we use the ratio of the sector angle to a full circle (360 degrees). The ratio is 270/360, which simplifies to 3/4.
Therefore, the volume of the partial cylinder is approximately:
V = (3/4)π(4^2)(10)
V ≈ (3/4) × 16π × 10
V ≈ 120π
Using the approximation π ≈ 3.14, the volume is approximately 376.8 cubic centimeters.