Circle + sphere - practice problems

Number of problems found: 18

Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
Float boya
A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/
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. The diameter of the circle that marked the water level on the surface of the ball was 8 cm. Find the diameter of John ball.
Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
What is bigger?
Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
Average speed
What is the average speed you have to move the way around the world in 80 days? (Path along the equator, round to km/h).
The Earth
The Earth's surface is 510,000,000 km². Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
Surveyors
Surveyors mark 4 points on the surface of the globe so that their distances are the same. What is their distance from each other?
The volleyball ball
The volleyball ball can have a circumference after inflation of at least 650 max 750 mm. What volume of air can this ball hold, if its circumference is the average of the minimum and maximum inflation of the ball.
Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
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.
Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
Sphere
Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
Horizon
The top of a lighthouse is 19 m above the sea. How far away is an object which is just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.]
Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
Sphere cuts
At what distance from the center intersects sphere with radius R = 91 plane, if the cut area and area of the main sphere circle is in ratio 3/6.

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Circle practice problems. Sphere practice problems.