Examples for secondary school students - page 98 of 232
Number of problems found: 4622
- Pyramid surface calculation
Calculate the surface area of a regular quadrilateral pyramid given: a= 3.2 cm h= 19 cm Method: 1) calculation of the height of the side wall 2) area of the base 3) shell areas 4) the surface of a regular quadrilateral pyramid - Cone surface calculation
The volume of a cone with a radius of 6 cm is 301.44 cm cubic. What is its surface? - Team placement calculation
Peter calculated the number of placement options with four teams, A, B, C, and D, in the first three places. He helped himself with a tree diagram. Complete the solution. - Line plane intersection
What is the sum of all coordinates of points at the intersection of the line p: x = -1-2t, y = 5-4t, z = -3 + 6t, where t is a real number, with the coordinate planes xy and yz? - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates [- 14; 0]? - Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Average speed
A car traveled from city A to city B at a speed of 40 km/h, then from B to C at 60 km/h, and finally from C to D at 50 km/h. Calculate the car's average speed over the entire route from A to D if the distance from A to B is 20% of the total distance and f - Table and chairs
Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chairs between them if people randomly choose their place? - Tiles
The tile is square and has a side of 15 cm. What dimensions can a rectangle composed of 90 tiles have so that no tile remains? - Trapezoid angle calculation
In the ABCD trapezoid: | AD | = | CD | = | BC | a | AB | = | AC |. Determine the size of the delta angle. - Trip distance calculation
The Macháček family went on a 3-day trip to Třeboň. They didn't want to get too tired but wanted to see a lot. Therefore, they drove at a walking pace, and at the end of the 3rd day, they measured 90 km on the speedometer. On the second day, they traveled - Pavel 3
Pavel has deposits in two accounts. One in a current account with an annual interest of 2% and the other in a savings account with an annual interest of 4%. Both deposits earned him CZK 1,000 per year. If Pavel transferred the deposit from one account to - Mushroom collection calculation
Vašek likes to go to the forest to pick mushrooms. He collected them successively for 3 days. Day 1 found seven less than Day 3. On the second day, he collected eight more than on the third day. He collected a total of 79 mushrooms. How much did he collec - The tourist
The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. However, after a 4 km walk, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re - Trapezoid perimeter calculation Find the points A1 B1 symmetric along the y-axis to the points A [-4,0] and B [-1,4]. Calculate the perimeter of the trapezoid AB B1 A1.
- Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°. - Vector equation
Let's v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7). Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1, c2, c3 and decide whether v, u, and w are linear dependent or independent - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Cuboid and ratio A cuboid has a volume of 810 cm³. The lengths of edges from the same vertex are in a ratio of 2:3:5. Find the dimensions of a cuboid.
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