Expression of a variable from the formula + right triangle - math problems

Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
Hexagonal pyramid
Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
The aspect ratio
The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
Two circles
Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
A rhombus
A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
Isosceles triangle 10
In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
A concrete pedestal
A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
Body diagonal
Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
Medians in right triangle
It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
Faces diagonals
If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
Tetrahedral pyramid
A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
Two chords
Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.

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