Cube practice problems - page 25 of 28

Number of problems found: 560

Inscribed sphere
How much % of the volume of the cube whose edge is 6 meters long is the volume of a sphere inscribed in that cube?
Percentage + sphere
A sphere G is inscribed in the cube K with the length a. A cube K1 is inscribed in sphere G. What percentage of the volume of cube K is made up of the volume of cube K1?
Thousand balls
We must create a thousand balls from a sphere with a diameter of 1 m. What will be their radius?
Mug in Cube Box
A cylindrical mug is packed in a 1-liter cube paper box. The mug is in close contact with all the walls of the cube. What volume is my mug?
Sphere area
A cube with an edge 1 m long is a circumscribed sphere (vertices of the cube lie on a sphere's surface). Find the surface area of the sphere.
Cylinder in a Cube
The cube has an edge length of 5 cm. This cube surrounds a rotating cylinder. Find the surface area of the shell and the volume of the cylinder.
Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm².
Cone in cube
The cube is an inscribed cone. Determine the ratio of the volume of the cone and cube. Please write the ratio as a decimal number and as a percentage.
Inscribed sphere
How much percent of the cube volume takes the sphere inscribed into it?
Shots
500 lead shots with diameter 4 mm are decanted into a ball. What is its diameter?
Cylinder
Calculate the dimensions of rotating cylindrical containers with volume 10 l if the container's height is equal to the base's diameter.
Inscribed
The cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
Cylinder - area
The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of the cylinder if its volume is 2 m³.
Cube from sphere
What largest surface area (in cm²) can have a cube that we cut out of a sphere with a radius 26 cm?
Equilateral cylinder
Find the radius and height (in centimeters) of an equilateral cylinder with a volume of 1 liter.
Surface of the cylinder
Calculate the cylinder's surface area when its volume is 45 l, and the base's perimeter is three times the height.
Surface area of cylinder
Determine the lateral surface of the rotary cylinder, which is a circumscribed cube with a 5 cm edge length.
Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone.
Pyramid in cube
In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid.
Balls
Three metal balls with volumes V₁=12 cm³, V₂=112 cm³, and V₃=59 cm³ were melted into one ball. Determine its surface area.

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