# Body volume - 7th grade (12y) - math problems

- The water tank

The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m^{2}? - AL wire

What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram. - Volume and surface area

Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm. - 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? - Water tank

300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach? - Oak trunk

Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³. - Tunnel boring

How much material did they dig when cutting the 400m long tunnel? The content of the circular segment, which is the cross section of the tunnel is 62m2. - Cone from cube

The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m^{3} - Rain

Garden shape of a rectangle measuring 15 m and 20 m rained water up to 3 mm. How many liters of water rained on the garden? - Cannonballs

Of the three cannonballs with a diameter of 16 cm, which landed in the castle courtyard during the battle, the castle blacksmith cast balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith c - The Earth

The Earth's surface is 510,000,000 km^{2}. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere. - Two rectangular boxes

Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface. - The largest

The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder? - Surface of the cube

Find the surface of the cube that has volume 1/1m3 2/0.001 m^{3}3/8000 mm^{3} - Half-filled

A cylindrical pot with a diameter of 24 cm is half-filled with water. How many centimeters will the level rise if we add a liter of water to it? - Wax candles

A company makes wax candles in the shape of a cylinder. Each candle has a diameter of 4 inches and a height of 7 inches. If the company used 7561.12 in^{3}of wax, how many candles did it make? Use 3.14, and do not round your answer - Height of the cylinder

The cylinder volume is 150 dm cubic, the base diameter is 100 cm. What is the height of the cylinder? - Nádoba

Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby? - Volume of the cone

Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm - The prison ball

Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.

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