Ratio + surface area - practice problems - page 2 of 3
Number of problems found: 50
- Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2:3. Calculate its volume if you know its area is 314 cm square. - Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Determine: 10182
The lengths of the edges of two cubes are in the ratio 1:2, determine: a) the ratio of the content of the wall of the smaller cube to the content of the wall of the larger cube. b) the ratio of the surface of the smaller cube to the surface of the larger - Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs lengths are at a 3:4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm².
- Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm. - Sphere radius
The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change? - Dimensions 7932
The volume of the block is 5760 cm³. For the dimensions of a given block, a: b = 4:3, b: c = 2:5 Calculate its surface. - Rectangle 7768
The base of a cuboid is a rectangle. The ratio of its length to width is 3:2. The length of the rectangle of the base is in the ratio of 4:5 to the height of the block. The sum of the lengths of all the edges of the block is 2.8m. Find: a) the surface of - Determine 7488
The lengths of the edges of the two cubes are in the ratio 2:3. Determine how many times the surface of the larger cube is larger than the surface of the smaller cube.
- Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Dimensions 6130
The aquarium dimensions are in the ratio a: b: c = 5:2:4. 6609 cm² of glass was used for its production. How many liters of water will fit in the aquarium if it reaches 5 cm below its edge? - Surface of cubes
Peter molded a cuboid of 2 cm, 4cm, and 9cm of plasticine. Then the plasticine was split into two parts in a ratio of 1:8. From each piece made, a cube. In what ratio are the surfaces of these cubes? - Cube edges
Find the cube edge length (in centimeters) that has a surface and volume expressed by the same numeric value. Draw this cube in a ratio of 1:2. - Ratio-cuboid
The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
- Circular 4690
The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout? - Cube
One cube has an edge increased five times. How many times will larger its surface area and volume? - Cuboid - ratios
The sizes of the edges of the cuboid are in the ratio of 2:3:5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid. - Surfaces 3793
The volumes of the two cubes are in the ratio of 27:8. What is the ratio of the surfaces of these cubes? - Cuboid - edges
The cuboid has dimensions in a ratio of 4:3:5. The shortest edge is 12 cm long. Find: The lengths of the remaining edges The surface of the cuboid The volume of the cuboid
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