Volume - high school - math problems

Number of problems found: 278

Ideal gas law
Assuming compression is according to the law pV = constant. Calculate the initial volume of gas at a pressure of 2 bar which will occupy a volume of 6 cubic meters when it is compressed to a pressure of 42 bar?
Dynamometer
What is the volume of a body that stretches a dynamometer in air, on which it is suspended by a force of 2.5 N, and if it is immersed in alcohol with a density of 800 kg/m ^ 3, does it tension the dynamometer with a force of 1.3 N?
The surface
The surface of the cylinder is 1570 cm², its height is 15 cm. Find its volume and radius of the base.
Above water surface
If we remove the stone from the water, we apply a force of 120N. How much force will we have to exert if we move the stone above the water surface? The density of the stone is 5000 kg/m ^ 3.
School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm ^ 3
Frustrum - volume, area
Calculate the surface and volume of the truncated cone, the radius of the smaller figure is 4 cm, the height of the cone is 4 cm and the side of the truncated cone is 5 cm.
Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
Confidence interval
A food testing laboratory in Abu Dhabi has been commissioned to carry out an estimate of the amount of olive oil contained in 1-gallon tins purchased from a range of international olive oil producers. The manufacturers state that the standard deviation of
Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm³, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. Calculate the area of the upper base.
The tetrahedron
Calculate the surface area and volume of a regular tetrahedron 4.9 cm high, the base edge has a length of 6 cm.
Consider
Consider all square prisms with a height of 10 cm. If x is the measurement of the base edge, in cm, and y is the volume of the prism, in cm³. Graph the function
Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
Pharmacist
The pharmacist had a 12 l vessel herbal lotion, which contained a 30% active ingredient. Her assistant poured 18 liters of herbal lotion containing 45% of the active ingredient into a container. What percentage of herbal lotion was produced?
Statistical survey
Write TRUE OR FALSE for each question: 1 Standard deviation is a measure of central location. 2. The most frequent observation in a data set is known as the mode. 3 The most passive method of data collection is observation. 4 Access time for secondary dat
The cylinder
In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
Spherical section cut
Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees.
Compressed gas
The pressure vessel contains a compressed gas at a temperature t1 = 27°C and a pressure p1 = 4 MPa. How much does its pressure change when we release half the amount of gas and its temperature drops to t2 = 15°C?
Hard cone problem
The surface of the cone is 200 cm², its height is 7 centimeters. Calculate the volume of this cone.