# Examples for 8th grade - page 22

- OPT

What is the perimerer of a right triangle with the cathetuses 20 cm and 13 cm? - Water inlets

Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after? - Two workers

Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker? - Four pupils

Four pupils divided $ 1938 so that the second received 20% less than the first, the third 1/6 less than a fourth and fourth $ 132 less than the first. How much money had each of them? - Cable car 2

Cable car rises at an angle 39° and connects the upper and lower station with an altitude difference of 345 m. How long is the track of cable car? - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-9,-8] and B[-8,0]? - Cubes

Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm^{2.}Determine the length of the edges of this cubes. - Triangular prism

Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume. - Diagonals

Rhombus has two diagonals e=11 dm and f=17 dm. Calculate the side angle and height of the rhombus. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - Monty Hall

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W - Area codes

How many 6 digit area codes are possible if the first number can't be zero? - Cuboid

Find the cuboid that has the same surface area as the volume. - Rhombus

Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 352 dm and the other diagonal BD has length 148 dm. - Certificate

There is 28 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 1.4643. How many students have mark 1 and how many mark 2? - Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 10 cm and a height v = 2.7 cm. - Pharmacy

At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 24 L of 36-percent solution. What amount of solution from each container is needed to mix? - Ladislav in Amsterdam

Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 2184. Calculate how many books Ladislav could buy at the price of 42 and 28 euros if he don't want fill whole home library and he can buy only 63 books? - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3.}Calculate the volume, surface and diameter of the sphere. - Park

In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.

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