Volume - 8th grade (13y) - math problems

Copper Cu wire
Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
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 m²?
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.
Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
The conical
The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
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.
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/m³
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
Diameter = height
The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
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.
Water mixing
There are 5 liters of water at 75°C in the pot, how much water at 10°C do we have to add to the resulting temperature of 55°C?
A bucket
A bucket has 4 liters of water in it when it is 2/5 full. How much can it hold?
The regular
The regular quadrilateral pyramid has a volume of 24 dm³ and a height of 45 cm. Calculate its surface.
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.
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?
Aircraft angines
The two engines of the aircraft are enough to supply the fuel for five hours of operation. However, one of the engines has a malfunction and thus consumes one-third more fuel. How long can the plane be in the air before it runs out of fuel? After an hour
Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
Wines
Eleven liters of white wine and eight liters of red wine cost a total of 1315 kc. 1 liter of white wine was 10 kc cheaper than a liter of red wine. How much is 1 liter of white and how much red wine?