Basic operations and concepts - math word problems - page 319 of 324
Number of problems found: 6465
- Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Road
A ratio of 1:19 gives the average climb of the road. By what angle does the road moderate climb? - Goat
The meadow is a circle with a radius r = 20 m. How long must a rope tie a goat to the pin on the meadow's perimeter to allow the goat to eat half of the meadow? - Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 119 m. How far is it from the other end of the fence? - Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - Cuboid surface ratio
The volume of the cuboid is 960 cm³. The lengths of the edges are in the ratio 1 : 3: 5. Calculate the surface area of the cuboid. - Dairy 2
The dairy meal is made up of a mixture of wheat bran and cotton. 40 kg of wheat bran cost sh.1250, and 50 kg of cotton cost sh.3250. 50 kg of a dairy meal is a mixture of 48 kg of wheat bran and 2 kg of cotton. Calculate the cost of a 1 kg dairy meal. - Doctors
The drug successfully treats 90% of cases. Calculate the probability that it will cure at least 18 patients out of 20. - Three shooters
Three shooters shoot, each time, on the same target. The first hit the target with 0.7, the second with 0.8, and the third with 0.9 probability. What is the probability of hitting the target: a) just once b) at least once c) at least twice - Climb of the road
At what angle does the road rise if the climb is 8%? They rounded up for tens of minutes. - Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°. - Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Rhombus
Internal angles of a rhombus are in ratio 2:5. How many times is the shorter diagonal longer than the side of the rhombus? - Larger sphere
The volume of the sphere is 20% larger than the volume of the cone. Find its surface if the volume of the cone is 320 cm³. - Block surface ratio The volume of the block is 7,500 dm³. The lengths of the edges are in the ratio 3: 4: 5. Calculate the surface area of the cuboid.
- Semicircles
In a rectangle with sides of 4 cm and 8 cm, there are two different semicircles, each with its endpoints at adjacent vertices and touching the opposite side. Construct a square such that two of its vertices lie on one semicircle, the other two vertices li - Ice rink
A rectangular ice rink measuring 15 m × 20 m needs to be covered with a layer of ice 4.5 cm thick. How many litres of water are needed to create the ice? - Road
The angle of a straight road is approximately 12 degrees. Determine the percentage of this road. - A ship
A ship has been spotted by two lighthouses, A and B, as shown in the figure. What is the distance from the ship to Lighthouse A to the nearest tenth? Figure - the distance between lighthouses A and B is 40 nautical miles. From A is seen in view angle 57°
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