# Area + expression of a variable from the formula - math problems

#### Number of problems found: 85

- Six painters

Six painters paint an area of 120 m^{2}in 4 hours. How long does it take for 12 painters to paint 480 m^{2}with the same performance? - Ratio of squares

A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares? - Extending square garden

Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m^{2}(square), it had the shape of a square again. How many meters has the length of each side of the garden been extended? - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Octagonal prism vase

0.7 l of water can be poured in an octagonal prism vase. What is the height of the vase, if the bottom has a area of 25 cm square and a thickness of 12 mm? - How many

How many m^{2}of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters, if we count 8% of the material for bending and waste? - 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)? - The funnel

The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel. - Wooden bowls

20 wooden bowls in the shape of a truncated cone should be painted on the outside and inside with wood varnish. We need 0.1 l of paint to paint 200 cm^{2}. How many liters of paint do we have to buy if the bowls are 25 cm high, the bottom of the bowl has a d - Calculate 6

Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - Triangular prism

The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm^{3}? And the surface cm^{2}? - Edge c

Find the edge c of cuboid if an edge a = 20 mm, b = 30 mm and surface area S = 8000 mm^{2}. - Edge of prism

The regular quadrilateral prism has a surface of 250 dm^{2}, its shell has a content of 200 dm^{2}. Calculate its leading edge. - Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m. - 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. - Rectangular base pyramid

Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters. - Dimensions of the trapezoid

One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm^{2} - 9-gon pyramid

Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.

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