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

#### Number of problems found: 448

- The surface

The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10cm. - The diamond

The diamond has an area S = 120 cm^{2}, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond. - Two gardens

The flower garden has a square shape. The new garden has the shape of a rectangle, and one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original garden dimensions and the new garden if both gardens' area i - Truncated pyramid

The truncated regular quadrilateral pyramid has a volume of 74 cm^{3}, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. Calculate the area of the upper base. - The rectangle

The rectangle has one side 8 cm smaller than the type. If you reduce the length by 6 cm and increase the width by 2 cm, you will get a square whose area is 400 cm ^ 2. What are the original dimensions of the rectangle? - A isosceles

A isosceles triangle has an area of 168 cm² and it's added height and base is 370 cm. What are the measurements of it's height and base? - The block

The block, the edges formed by three consecutive GP members, has a surface area of 112 cm². The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block. - Side and diagonal

Find the circumference and the area of the rectangle if given: side a = 8 cm diagonal u = 10 cm. - Base diagonal

In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - The length 2

The length of a rectangle is 12y² – 15y + 8 and the width is 7y – 11. Find the area of the rectangle - Surface and volume - cube

Find the surface and volume of a cube whose wall diagonal is 5 cm long. - Metal washers

Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet. - Outside point

The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4? - The volume

The volume of the cone is 94.2 dm³, the radius of the base is 6 dm. Calculate the surface of the cone. - Truncated pyramid

Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm. - What is

What is the height of a cylinder whose surface size is 602.88 cm² and the content of its shell is 376.8 cm²? - The cylinder

In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder. - Rotary cylinder

In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height. - Pentagonal pyramid

The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid. - Truncated cone

Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm and side s = 10 cm.

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Area - practice problems. Expression of a variable from the formula - practice problems.