Body volume - math word problems
- 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?
- 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?
- Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
- Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
- Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
- Support colum
Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
- Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
- Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
- Cuboid and ratio
Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
- 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.
- Cylindrical tank
Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
- Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
- Water reservoir
The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
- Water tank
The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m3. Calculate how many kg of copper and zinc a cube contains.
- Gasoline tank cylindrical
What is the inner diameter of the tank, which is 8 m long and contains 40 cubic cubic meters of gasoline?
- The cylinder base
The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
- Cylinder twice
If the radius of the cylinder increases twice, and the height is reduced twice, then the volume of the cylinder increases (how many times?):
- Copper plate
Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg