an oblique cylinder has a radius of 10 units and slant length of 26 units. what is the volume of the…

Explanation:

Step1: Find the height of the cylinder

Use the Pythagorean - theorem. The slant length (l = 26) units and radius (r = 10) units. Let the height be (h). We know that (h=\sqrt{l^{2}-r^{2}}) (assuming the right - triangle formed by the radius, height and slant length). But for the volume of an oblique cylinder, we can use the fact that the volume of an oblique cylinder is the same as that of a right - cylinder with the same base area and height. First, we need to find the height of the equivalent right - cylinder. Using the Pythagorean theorem: (h=\sqrt{26^{2}-10^{2}}=\sqrt{(26 + 10)(26 - 10)}=\sqrt{36\times16}=\sqrt{576}=24) units.

Step2: Calculate the volume of the cylinder

The volume formula of a cylinder is (V=\pi r^{2}h). Substitute (r = 10) and (h = 24) into the formula. (V=\pi\times10^{2}\times24=\pi\times100\times24 = 2400\pi) cubic units.

Answer:

(2400\pi) cubic units