# Sphere - math word problems

- Pebble

The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm. - Cube in a sphere

The cube is inscribed in a sphere with volume 3234 cm^{3}. Determine the length of the edges of a cube. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - Sphere

The surface of the sphere is 12100 cm^{2}, and weight is 136 kg. What is its density? - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Spherical cap

From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere? - Earth parallel

Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km. - Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r_{1}=31 cm, r_{2}=92 cm and its distance v=25 cm. - Hollow sphere

Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm^{3}), if the inner diameter is 14 cm and wall thickness is 3 mm. - Balls

Three metal balls with volumes V_{1}=71 cm^{3}V_{2}=78 cm^{3}and V_{3}=64 cm^{3}melted into one ball. Determine it's surface area. - Cube in ball

Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere? - Balls

Ping pong balls have a diameter of approximately 5.1 cm. They are sold in boxes of 10 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled. - Sphere in cone

A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions. - Sphere A2V

Surface of the sphere is 241 mm^{2}. What is its volume? - Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Hollow sphere

Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m^{3} - Spherical segment

Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment. - Sphere and cone

Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone? - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.

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