Units - examples
- Three segments
The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
- Two cyclists 2
At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,.
- A company
A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
- Regular triangular pyramid
Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
- Quadrangular pyramid
The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
- Acid evaporation
How many kilograms of water do we have to evaporate from 100 kg of 32% acid to make it 80% concentration?
- Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
- Father and daughter
When I was 11 my father was 35 year old. Now, father has three times older then me. How old is she?
Katy had two dogs. The first one ate a pack of granules a week and the other two times longer. Katka bought them two bags of granules. How long does it last for both dogs?
- Journey 5
A man has to do a journey of 84km in 3 hours. He travels the first 30km at 20km/hr. At what rate must he travel the remaining distance to complete his journey on time?
- Three painters
One painter would have painted the fence for 15 hours, the second in 12 hours. The plot had to be painted in four hours, so they called the third one, and all worked together. For what time would the third painter paint fence the fence alone?
- Solid food
Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 of
The area of a 25 inch TV screen is 300 inch² the area of a 40 inch TV screen is 768 inch². The area of the smaller screen is what percent of the area of the larger screen?
- Car crash
After a traffic accident, police measured 1.16 permille of alcohol in the driver's blood. What amount of alcohol did the driver have in the blood when about 5 kg of blood circulates in the human body?
- Vertices of a right triangle
Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle
Grandfather gathered fresh mushrooms. The fifth was wormwood, and it was thrown away, the other dried up. He obtained 720 grams of dried mushrooms. How many kilograms did the grandfather collect, and by drying the mushrooms they lost 75% of their weight?
- Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
Caleb is making lemonade for a party. He has 5 gallons of lemonade. He is putting 1/3 cubic inch of lemonade in a cup for each guest. How many guests are going to be at the party?
- Milo lifted
Milo lifted 65 lb 6 times and Jeremy lifted 50 lb 9 times. Which one lifted the most weight?
- Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?