Percentages + body volume - math problems

Kostka
Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
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?
Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm². Find the area of the
Hectoliters
How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
Inscribed sphere
How many percents of the cube volume takes the sphere inscribed into it?
Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
Water tank
A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
Volume and body diagonal
Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
Volume increase
How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
Sugar cubes
The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured?
Ice and water
We want to cover rectangular rink with dimensions of 55 m and 25 m with 4cm thick layer of ice. How many liters of water we need if after freezing water increases its volume by 10%?
Fuel economy
How many kilometers is sufficient petrol in the cylinder fuel tank with a diameter 40 cm and the base of tank length 1 m, when it is filled to 60% and if the car consume 15 liters per 100 km?
Cuboid enlargement
By how many percent increases the volume of cuboid if its every dimension increases by 30%?
Vintner
How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number
Inscribed sphere
How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent?
Roof 8
How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.