Pythagorean theorem - math word problems - page 54 of 68
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:c2 = a2 + b2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
A common proof of the Pythagorean Theorem is called the "area proof". To prove the theorem using this method, we can create a square with side length c and two smaller squares with side lengths a and b, as shown in the figure. We can then place the smaller squares next to each other to form a rectangle with area a x b. We can then see that the area of the square with side length c is equal to the sum of the areas of the smaller squares, which is equal to the area of the rectangle. This demonstrates that c2 = a2 + b2, as stated in the theorem.
Another proof is Euclidean proof which is based on the Euclidean geometry and construction of a line segment that is c and perpendicular to the line segment of a and b.
Number of problems found: 1343
- Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. What are the volume of the segment and the surface of the segment? - Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. - 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. - Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm.
- Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Triangular prism
The base of the perpendicular triangular prism is a right triangle with a leg length of 5 cm. The area of the largest sidewall of its surface is 130 cm², and the body's height is 10 cm. Calculate its volume. - Stadium
A domed stadium is shaped like a spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the dome's height at its center to the nearest tenth of a meter. - Cap
A rotating cone shapes a jesters hat. Calculate how much paper is needed for the cap 54 cm high when the head circumference is 47 cm. - Quadrilateral 83254
What is the volume of a regular quadrilateral pyramid if its base edge a = √18 cm and side edge b = 5 cm?
- Precisely 82088
A regular helix is drawn on the shell of the cylinder such that it wraps around the cylinder precisely three times (that is, the point where it touches the upper base is exactly above the point where it touches the lower base). If the diameter of the cyli - Quadrilateral 36061
In a regular quadrilateral pyramid, the length of the base edge is a = 8 cm, and the length of the side edge is h = 17 cm. Calculate the surface of the pyramid. - Diagonal 8192
Find the volume and surface of a cube if you know the length of its body diagonal u = 216 cm. - Dimensions 6264
Calculate the length of the body diagonal of a block whose dimensions are a = 5cm, b = 6cm, c = 10cm. - Decimetres 4163
Determine the length of the body and wall diagonals of the cube, the volume of which is equal to 0.343 decimetres. Also, calculate its surface.
- Triangular 46641
The regular triangular pyramid ABCDV has a base edge length of 8 cm and a height of 7 cm. Calculate the pyramid's surface area and volume. - Diameter 44511
The tower's roof has the shape of a cone with a base diameter of 12 m and a height of 8 m. At least how many square meters of roofing are needed to cover? - Calculate 32133
The cube has an area of 486 dm². Calculate the length of its side, its volume, the length of the body, and wall diagonals. - Calculate 30971
Calculate the cone's surface and volume if its base diameter is 1 dm and the side length is 13 cm. - Calculate 30961
Calculate the cone's surface and volume if its base diameter is 12 cm and the height is 150 mm.
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