Hemisphere practice problems
A hemisphere is exactly half of a sphere, formed by cutting a sphere with a plane passing through its center. The flat circular face has radius r equal to the sphere's radius, while the curved surface is half the sphere's surface area. The volume of a hemisphere is V = (2/3)πr³, which is half the sphere's volume. The curved surface area is 2πr², and the total surface area including the flat base is 3πr². Hemispheres appear in architecture (domes), geography (Earth's northern and southern hemispheres), and various everyday objects. Understanding hemispheres involves visualizing three-dimensional geometry, calculating curved and flat surface areas, and applying volume formulas. They represent important examples of composite solids in geometry.Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 28
- A hemispherical
A hemispherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain? - Water 70 Water is poured into a hemisphere-shaped bowl at a rate of 5m³ per second. If the bowl has a depth of 8m, how long does it take to fill up the bowl to the rim?
- Spheres - ratios
The surface area of two spheres are in the ratio 1 : 4 . Find the ratio of their volumes. - A solid
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid . - A capsule
A medicine capsule is a cylinder with two hemispheres stuck to each end. Its length is 14 mm, and its diameter is 5 mm. Find its surface area. - Tent - spherical cap
I have a tent in the shape of a spherical cap. Assume we want the volume to be 4 cubic meters, to sleep two or three people. Assume that the material making up the dome of the ten is twice as expensive per square as the material touching the ground. What - Hemisphere of ice-cream
The ice cream maker sold 6l of ice cream a day. How many hemisphere-shaped portions with a diameter of 6 cm could he make from the ice cream sold? - A semi-circular
A semi-circular fishbowl is filled with water and has a diameter of 10 feet. What is the total water weight to the nearest pound in the tank if water weighs 62.5 pounds per cubic foot? - Cathedral roof sphere
Cathedral height is 110 m, sphere weight 6000 kg, dome diameter 43 m, crane arm length 25 m a) what was the diameter of this sphere? b) how much mechanical work had to be done to lift it to the designated place? - Hemispherical dome
What is the coverage area of the painting of a hemispherical dome with a diameter of 8 m? - Calculation - hemisphere The roof is shaped like a hemisphere with a diameter of 8 m. Calculate how much m² of roofing is needed to cover the entire top if we count 15% for waste and residues and round the result to tenths of m². Use the constant pi rounded to two decimal places
- Ball screen
The diameter of the ball screen is 30 cm. If we add 5% of the material to be sewn, how many m² of fabric do we need to make? - Observatory's dome
In our city, they decided to reconstruct the observatory's dome and cover it with sheet metal. At least how many square meters of sheet metal will they need if the dome is in the shape of a hemisphere with a diameter of 6m? - Half-sphere roof
The roof above the castle tower has the shape of a 16 m diameter half-sphere. What is this roof's cost if the cost of 1 square meter is 12 euros and 40 cents? - Sphere cut area
We cut a sphere with a diameter of 10 dm into two equal parts. Calculate the area of the cut. - Planetarium dome area
The planetarium's dome is shaped like a hemisphere with a diameter of 17 m. Determine the size of the projection area - Observatory
The observatory dome has the shape of a hemisphere with a diameter d = 10 m. Calculate the surface. - Hemisphere - roof The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of thinner are used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of thinner will paint
- The observatory The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal need to be covered to cover it, and must we add 15 percent to the minimum amount due to joints and waste?
- Spherical bowl
The bowl, in the shape of part of a spherical surface, has a diameter of 28 cm at the top edge and is 8 cm deep. What is the total volume of the bowl? How much water would you have to pour into the bowl to fill it halfway?
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