Real numbers - practice problems - page 8 of 9
Number of problems found: 165
- Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long. - Events
Event W has the probability of 0.57. What is the probability that the event W occurs in 2, 6, 5 try? - Angles
Find the interior angles of a rhombus with area 72 cm² and perimeter 48 cm. - Web server
Calculate how many average minutes the web server is unavailable a year if the availability is 99%. - ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - Cone A2V
The lateral surface of a cone, when unrolled flat, forms a circular sector with a central angle of 126° and an area of 415 cm². Calculate the volume of the cone. - Rectangle
The rectangle is 21 cm long and 38 cm wide. Find the radius of the circle circumscribing the rectangle. - Area of RT
Calculate the area of a right triangle in which the hypotenuse has length 14 and one of the segments that the altitude creates on the hypotenuse has length 5. - Pyramid roof
3/5 of the lateral surface area of a regular quadrilateral pyramid with base edge 9 m and height 6 m has already been covered with roofing. How many square metres still need to be covered? - Area of RT
A right triangle has segments on the hypotenuse (created by the altitude) of lengths 15 cm and 9 cm. Determine the area of this triangle. - Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface? - Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 119 m. How far is it from the other end of the fence? - Rotation
A right triangle with legs 11 cm and 18 cm is rotated around the longer leg. Calculate the volume and surface area of the cone formed. - Axial section
The axial cross-section of a cone is an equilateral triangle with an area of 208 km². Calculate the volume of the cone. - Spherical cap
From a sphere with radius 26, a spherical cap was cut. Its height is 2. What part of the volume is a spherical cap from the whole sphere? - Regular 5-gon
Calculate the area of the regular pentagon with side 16 cm. - Triangle TBC
TBC is an isosceles triangle with base TB, base angle 75°, and equal legs |TC| = |BC| = 35. How long is the base TB? - Movement
Two cyclists set off from an intersection of two perpendicular roads, each taking a different road. One travels at an average speed of 16 km/h and the other at 25 km/h. Determine the distance between them after 20 minutes of cycling. - Gutter
How much metal is needed to produce 60 pieces of gutter pipes with the diameter 17 cm and length of 6 m? The plate bends add 6% of the material.
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