Practice problems of the volume - page 22 of 118
Volume is the measure of the space that a body fills or occupies. The basic SI unit of volume is the cubic meter. It is the volume of a cube with an edge of one meter, i.e., 1 m x 1 m x 1 m. Significant another unit is 1 l (one liter), 1 m3 = 1000 l applies. One hectoliter (1 hl) is 100 liters.Volume is always the third power of length. Or volume = area times length. For example, the volume of the cube is a3, and the prism's volume is S*h (the area of the base times the height). The volume of rotating bodies (sphere, cone) can be derived in high school by integration. The pyramid's volume is always 1/3 of the prism's volume. We calculate the volume of the truncated bodies either with a formula or simply by subtracting the volumes of the two bodies.
Number of problems found: 2345
- Difference 66354
A circle is inscribed in a square with a side of 12 cm so that it touches all its sides. Calculate the difference between the area of the square and the circle. - Right-angled 66344
From a square with a side of 4 cm, we cut four right-angled isosceles triangles with right angles at the square's vertices and with an overlap of √2 cm. We get an octagon. Calculate its perimeter if the area of the octagon is 14 cm². - Deciliters 66324
We placed the largest possible lead cylinder in a 1-liter cube container. How many deciliters of water will now fit in the container? - Quadrilateral 66294
Calculate the surface and volume of a quadrilateral prism if given: the area of the base is 40 cm square, the bottom of the base is k = 8 cm, and the height of the prism is 1.3 dm (the bottom is a rectangle) - Enlarge 66284
We will enlarge the line 8 cm long in the ratio of 7:4. How long in cm will the new line be? - Perpendiculars 66274
The perpendiculars of a right triangle have lengths of 30 cm and 40 cm. What is the height of the triangle? - Calculate 66254
Calculate the volume and surface of a regular hexagonal prism with a height v = 2cm and a base edge a = 8cm. - Flowing 66174
How long in an hour will a 30m, 15m, and 2m pool be filled with water flowing at 900l / min if it is 90% full? - Circumference 66134
The isosceles trapezoid ABCD has an area of 36 cm². One of its bases is two times longer than the other. Height is 4 cm. Calculate the circumference of the trapezoid. - Cylindrical 66114
The cylindrical vase has a volume of 1 l. Calculate the height of the vase if its base has an area of 0.5 dm². - Mr. Bradshaw
Mr. Bradshaw is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 5 meters high. The ladder's base is 1 meter away from the house, where Mr. Bradshaw's son is holding it steady. How long is - Interest 66024
How much do I have to save per month to save CZK 100,000 in 5 years if the interest rate is 4%, the interest period is one month, and the interest tax is 15%? - Vertically 65984
We threw the stone vertically upwards at a speed of v = 15m. s-1. How long will it be at a) 10 m, b) 12 m? - Block-shaped 65944
We have a block-shaped container measuring 20 cm x 30 cm x 45 cm. How many will 5 cm cubes fit in it? - Calculate 65924
Calculate the volume of a cylinder whose base has a diameter d = 22 cm and its height is 1.7 dm. - A tank
A tank is 7/9 full of water,1/5 of the tank is drawn in the morning, and 1/3 is drawn in the evening. What fraction of water is still in the tank? - Centimeters 65884
The plastic bucket has the shape of a cylinder with a diameter of 25 cm and a height of 40 cm. How many square centimeters are needed to produce it? How many liters does it contain when filled 5 cm below the rim? - Chocolate 65824
Robert has 8.2 cm, 3.1 cm, and 0.8 cm chocolate. Norbert has 0.4 cm, 5 cm and 7.9 cm chocolate. Which one has more chocolate, and how much? - Calculate 65804
Calculate the surface and volume of a rotating cone, the base of which has a diameter of 6 cm and its height of 4 cm. - Increase 65794
The area of the square is 36 cm². What will be the area of the square if we increase the length of a side by 25%?
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