Area of shape + expression of a variable from the formula - math problems
Number of problems found: 199
- 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?
- Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
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?
- Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
- Quadrilateral pyramid
A regular quadrilateral pyramid has a volume of 24 dm3 and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
- Quadrilateral pyramid
Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
- In the
In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
- Height to the base
The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base.
- Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism
- 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.
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
- 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.
- 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 cm2
- Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
- The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
- The right triangle
The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
- Cross five
The figure on the picture is composed of the same squares and has a content of 45cm². What's its perimeter?
- 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.
- Edge of prism
The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
- 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.