Pythagorean theorem + expression of a variable from the formula - practice problems - page 28 of 29
Number of problems found: 580
- An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter. - Truncated cone
Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm, and side s = 10 cm. - Rectangular base pyramid
The pyramid has a rectangular base of 2.8 m and 1.4 m and a height of 2.5 meters. Calculate an area of the shell of the pyramid. - Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³.
- Slant height
The cone's slant height is 5cm, and the radius of its base is 3cm, so find the cone's volume. - Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - Calculate 8326
Calculate the cone shell with a base diameter of 40 cm and a cone height of 50 cm. - Hexagonal 6424
Calculate the volume and surface of a regular hexagonal prism, the base edge of which is 5 cm long and its height is 20 cm. - The pyramid
The pyramid with a square base is 50 m high, and the sidewall height is 80 m. Find the edge of the base of the pyramid.
- Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base? - A concrete pedestal
A concrete pedestal has the shape of a right circular cone and a height of 2.5 feet. The diameters of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the pedestal's lateral surface area, total surface area, and volume. - Spherical cap 4
What is the surface area of a spherical cap, the base diameter of 20 m, and the height of 2.5 m? Calculate using the formula. - Quadrangular pyramid
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm, and volume V = 1000 cm³. Calculate its side and its surface area.
- A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall. What is the diagonal S of the bottom side? What is the length of the body diagonal R? - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Quadrangular prism
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal 22 cm. - Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - Calculate 82458
Calculate the volume of a cube with a wall diagonal of u = 20 cm.
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