Math practice for 13 year olds - page 178 of 414

Number of problems found: 8280

The amphitheater
The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, and the stage forms the diameter of the semicircle. Which spectators, P, Q, R, S, and T, see the stage at the greatest viewing angle?
Totem shed fitting
The boys wanted to store their hand-made totem 5.1 m high in the block-shaped shed, which measures 4 m, 3 m, and 2 m, for the winter. Will it fit in there at all?
Average speed
The car drove from city A to city B at 40 km/h and back to city A at a speed of 80 km/h. What was the average speed of the car?
Škoda cars
At 8:30 AM, car Škoda 120 started from Prievidza at 60 km/h toward Bratislava. At 9:00, we started from Prievidza in the same direction as Škoda Rapid at 90 km/h. Where and when will Škoda Rapid catch up with Skoda 120?
Car departure time
A bus left Žilina towards Bratislava at 9:00 a.m. at an average speed of 60 km/h. After a certain time, a Škoda Superb set off from Žilina in the same direction at a speed of 100 km/h and overtook the bus after 45 minutes. When did Škoda leave Žilina?
Sidewalk worker
Workers are building a new sidewalk while revitalizing the housing estate. Six workers will do the work in 12 days, but this is a problem because the sidewalk must be completed in 10 days to complete the work on time. How many workers must be hired to com
Avia car
Avia left Prague at 7:00 a.m. at 80 km/h. When she was near Trnava (60 km from Bratislava), a Volkswagen Passat set off on the same road from Bratislava at a speed of 120 km/h. When and at what distance from Trnava did the Volkswagen Avia catch up?
The resistance
What is the resistance of an aluminum wire, 0.2 km long and 10 mm in diameter?
The caravans
At 6:00 in the morning, a caravan set out of the oasis at a speed of 1.5 miles per hour. Two hours later, a second caravan followed her at 2.5 miles per hour. When did the faster caravan run slower? How far from the oasis?
Square circle area
A circle describes a square with a side of 8 cm. Calculate the area of the rest of the circle if we cut out the square.
Class student
N boys go to class. There are 13 more girls. Today, 4 girls and 5 boys are missing. Thus, how many students in this class are in school today?
Slices of ham
If 17 slices equal 70 calories, how many calories are in 5 slices?
Savings spending
Helen and Barbara had 1,500 CZK saved together at the end of January. After Helen spent CZK 318 from her savings and Barbara spent CZK 249 from her savings in February, Helen had twice as much CZK saved as Barbara. How much money did they have at the begi
Body diagonal
Calculate the length of the space diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
Triangle line
In the triangle ABC, the line tb = | is given BB1 | Calculate the length of this line if B1 T | = 3 cm.
Two companies
Company A can fulfill the order in 12 days, and company B can fulfill the same order in 18 days. If only company A works on the order for the first two days and then both companies work on it for the remaining days, how many days will the order be fulfill
Car distance
Two opposite cars passed on the way and continued. One car drove 17.5 m in 1 second and the other 15.25 m. How far will these cars be in half an hour?
Trees
Two-fifths of the trees in the orchard are apple trees, one-sixth a pear. The remaining 26 trees are cherries. How many pears are in the orchard?
Karolína
Carolina chose five bodies from the kit - white, blue, and gray cubes, a blue cylinder, and a white triangular prism. How many different roof towers can be built one by one if all the blue bodies (cube and cylinder) are not placed on top?
Aluminum plate forces
An aluminum plate with a volume of 200 cm³ sinks in water. Determine the gravitational force exerted by the Earth on the plate. Determine the buoyant force that acts on a plate immersed in water. Compare the magnitudes of these forces and justify whether

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