Area of shape + volume - math problems

Number of problems found: 143

An experiment
The three friends agreed to the experiment. At the same time, they all took out an empty cylindrical container on the windowsill and placed it so that it was horizontal. Everyone lives in a different village, and each used a container with a different bot
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.
Triangular prism
The regular triangular prism has a base edge of 8.6 dm and a height of 1.5 m. Finf its volume and surface area.
Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
The resistance
What is the resistance of an aluminum wire 0.2 km long and 10 mm in diameter?
Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
Hexaprism container
Calculate the volume and surface in the shape of a regular hexagonal prism with a height of 1.4 m with a base edge of 3dm and a corresponding height of 2.6 dm.
Iglu - cone tent
The cone-shaped tent is 3 m high, the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring) if 20% needs to be added to the minimum amount due to cutting waste? b)
The pool
The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom?
Copper winding
Calculate the current flowing through the copper winding at an operating temperature of 70°C. Celsius, if the winding diameter is 1.128 mm and the winding length is 40 m. The winding is connected to 8V.
Swimming pool
A swimming pool 30 meters long is filled with water to a depth of 1 meter at the shallow end, and 5 meters at the deep end and abcd the vertical area of the pool has the shape of a trapezium with the area given by S(abcd)= 1/2 (ab + cd) x ad. What is the
Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm.
Wooden bowls
20 wooden bowls in the shape of a truncated cone should be painted on the outside and inside with wood varnish. We need 0.1 l of paint to paint 200 cm². How many liters of paint do we have to buy if the bowls are 25 cm high, the bottom of the bowl has a d
Diver
Please calculate using Pascal's law. The window of the diving helmet has a surface content of about 7dm². Calculate what pressure force acts on the window at a depth of 20 meters below the water surface.
Surface of the cone
Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.
Volume of the cone
Calculate the volume of the cone if the content of its base is 78.5 cm² and the content of the shell is 219.8 cm².
9-gon pyramid
Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
Octagonal prism vase
0.7 l of water can be poured in an octagonal prism vase. What is the height of the vase, if the bottom has a area of 25 cm square and a thickness of 12 mm?
Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
Hexagonal prism
Calculate the volume and surface of a regular hexagonal prism with the edge of the base a = 6 cm with the corresponding height v1 = 5.2cm and the height of the prism h = 1 dm.