Mathematics stereometry

[Guest]

Hey, I need some help with quite challenging maths exercises. The solutions of how to find those would be very needed, because my mind is close to blowing up .

Cilinder height is 2 m and bottom radius is 7 m. Inside the cilinder is a square, which is inclined by the axis and its corners are located on both bottom circles. Find the square side length. (I literally have no clue on where to even start here)

Cone height is 10 cm and bottom area is 25 π square-cm. Find the area of the section which is parallel with the bottom, if the section is 4 cm away from the bottom of the cone. (I found the bottom radius with 25 π=πr² and the r=5cm. With the pythagoras I found the side of the triangle which came as √125(cm). From that point I am stuck)

Triangles sides are 12 cm, 17 cm and 25 cm and its spinning around its closest side. Find the area of the new object. (I tried to use Heron formula, but I have no clue what to continue with there)

If pictures of solutions cant be put here, I would be grateful to death if you sent them to me at my email: andreandyb@gmail.com

Thanks in advance and have a wonderful day!

[Guest]

Cilinder ("cylinder") height is 2 m and bottom radius is 7 m.[/quote]
"Bottom radius"? Isn't the top radius also 7m?

Inside the cilinder is a square, which is inclined by the axis

I don't know what "inclined by the radius" means!

and its corners are located on both bottom circles.

Both "bottom circles"? How are there two "bottom circles"?

Find the square side length. (I literally have no clue on where to even start here)

If you simply mean that all four corners of the square are on the circle, then the diagonals of the square are diameters of the circle so are 14 m long. The diagonals are the hypotenuse of a right triangle with both legs of length s. Use the Pythagorean theorem to find the side length, s.

Cone height is 10 cm and bottom area is 25 π square-cm. Find the area of the section which is parallel with the bottom, if the section is 4 cm away from the bottom of the cone. (I found the bottom radius with 25 π=πr² and the r=5cm. With the pythagoras I found the side of the triangle which came as √125(cm). From that point I am stuck)

Yes, the bottom radius is 5 cm. so the bottom diameter is 10.. Seen from the side, the cone is a triangle with height 20 cm and base length 10 cm. A line draw parallel to the base "4 cm from the bottom" (so 10- 4= 6 cm from the top of the cone) makes a "similar triangle" with height 6 instead of 10. All lengths in this smaller triangle are [tex]\frac{6}{10}= \frac{3}{5}[/tex] the corresponding length in the larger triangle. The base of the smaller triangle has length [tex]\frac{3}{5}(10)= 6 cm[/tex]. The bottom of this smaller cone is a circle with diameter 6 cm so radius 3 cm. What is its area?

Triangles sides are 12 cm, 17 cm and 25 cm and its spinning around its closest side. Find the area of the new object.

I have no idea which side is "closest". Closest to what? And do you want the surface area? Or do you actually want the volume?