# High school + Pythagorean theorem - examples

1. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
2. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
3. Cable car Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
4. Spherical cap 4 What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
5. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
6. Cube in a sphere The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
7. Axial section Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
8. Circle chord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
9. Rectangle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
10. Trigonometric functions In right triangle is: ? Determine the value of s and c: ? ?
11. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
12. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
13. Triangle SAS Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
14. Square Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
15. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
16. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
17. Gimli Glider Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
18. River From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
19. Rectangle In rectangle with sides 10 and 8 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
20. Square and circles Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.

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Pythagorean theorem is the base for the right triangle calculator.