# Expression of a variable from the formula - math word problems

- Two hemispheres

In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)? - Wire fence

The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure? - Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4. - The farmer

The farmer calculated that the supply of fodder for his 20 cows was enough for 60 days. He decided to sell 2 cows and a third of the feed. How long will the feed for the rest of the peasant's herd last? - The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm^{2}. Calculate the length of the leg b and the median t2 to side b. - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord? - In a

In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides. - Closed circuit

In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage. - Library

New books were purchased for the library. Five-eighths were professional books, one-fifth were encyclopedias, and 231 books were dictionaries. How many professional books were there? - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - What is bigger?

Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm? - Double price reduction

The price of TV has been reduced twice. First by 15% and later by another 10% of the reduced price. After this double price reduction, the TV was sold for 8,874 crowns. What was the original price of the TV? - The angles ratio

The angles in the ABC triangle are in the ratio 1: 2: 3. find the sizes of the angles and determine what kind of a triangle it is. - A map

A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field? - Water tank

300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach? - Wallpaper

3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide? - Cone from cube

The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m^{3} - Diameter = height

The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume. - The Earth

The Earth's surface is 510,000,000 km^{2}. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere. - Spherical cap

The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.

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