Equation + surface area - practice problems
Number of problems found: 54
- Calculate 415
Calculate the cuboid's dimensions if the sum of its edges is 19cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - Cylinder 82991
Please express r from the formula for the surface of the cylinder. - Cylinder-shaped 81512
A truncated cone-shaped part with base radii of 4 cm and 22 cm is to be recast into a cylinder-shaped part of the same height as the original part. What base radius will the new part have? - Expressed 79474
The length of the cube's edge in cm is expressed as a natural number. Its volume is greater than 100 and less than 200. Calculate the surface area of the cube.
- Calculate 74024
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - An equivalent
An equilateral triangle has the same perimeter as a rectangle whose sides are b and h (b > h). Considering that the area of the triangle is three times the area of the rectangle. What is the value of b/h? - Quadrilateral 70294
The edge lengths of a quadrilateral prism are in the ratio a: b: c = 2:4:5. The surface of the prism is 57 cm². Calculate the volume. - Calculate 62864
The block volume is 1440 cm3, its surface is 792 cm2, and the area of one of its walls is 92 cm². Calculate the lengths of its sides. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls.
- The surface
The surface of the cylinder is 1570 cm²; its height is 15 cm. Find the volume and radius of the base. - 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 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. - 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.
- Hard cone problem
The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone. - Shell area cy
The cylinder has a shell area of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder. - The cylinder
The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder. - Rectangular 26641
The area of the work surface of the rectangular table is 70 dm2, and its perimeter is 34 dm. Determine (in dm) the length of the shorter side of this table. - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube.
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