Question

A cylinder has an elliptical base with major semiaxis length of 6 cm and minor semiaxis length of 4 cm. its altitude is 7.5 cm. find the volume of the cylinder. (hint: volume of the cylinder = area. of base × altitude.) volume (to the nearest tenth) = a0 cm 3.

Answer 1

180π cm³

Explanation:

The formula for the area of an ellipse with major axis a and minor axis b is

A = π·a·b.

Here, that area is A = π(6 cm)(4 cm) = 24π cm².

Multiplying this base area by the altitude, 7.5 cm, results in the volume:

V = (24 cm²)·π·(7.5 cm) = 180π cm³

Answer 2

565,5 cm³

Explanation:

To calculate the volume of a cylinder we have to found the area of the base and multiply by the altitude of the cylinder. As the base is elliptical, the area is given by:

`A = a*b*\pi`, where a is the major axis and b the minor axis. Thus:

`A=6*4*\pi =75.39 cm^2`

And,

`V = A*h = 75.39*7.5 = 565.48 cm^3`.

Rounding to the nearest tenth: 565.5 cm³