Examples for secondary school students - page 12
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1115 cm3 and a base radii r1 = 7.9 cm and r2 = 9.7 cm.
- Reservoir + water
Reservoir completely filled with water weighs 12 kg. After pouring off three quarters of the amount of water weights 3 kg. Calculate the weight and volume of the reservoir.
- Built-up area
John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?
- Right triangle
Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm.
- Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
- Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
- MO - triangles
On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se
From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
- Airplane navigation
An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
- Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
- Trapezoid - diagonal
Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
- House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
- Wire D
Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
- Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
- Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.