Volume + expression of a variable from the formula - practice problems

Number of problems found: 291

Sphere volume formula
If V=4/3 π r³, find, the value of V when r = 7, the value of r when V=113 1/7
The height of prism
The base of the perpendicular prism is formed by a right triangle with perpendiculars 30 cm and 40 cm long. This prism has the same volume as a cube with an edge length of 3 dm. Find its height in cm.
Slant height 2
A regular triangular pyramid with a slant height of 9 m has a volume equal to 50 m³. Find the lateral area of the pyramid.
Equilateral cylinder
Find the radius and height (in centimeters) of an equilateral cylinder with a volume of 1 liter .
Height of the prism
The volume of the quadrilateral prism is 723.6 cm³. The base of this prism is a rhombus with a side 9 cm long and a corresponding height of 6.7 cm long. Find the height of the prism.
Cost structure
You are currently trying to decide between two cost structures for your business: one that has a greater proportion of short-term fixed costs and another that is more heavily weighted to variable costs. Estimated revenue and cost data for each alternative
Tank B
Tank B has the same volume as Tank A. The volume of one section of Tank B is 4545 cubic feet. What is the volume, in cubic feet, of the other section of Tank B? Total volume of both tanks A+B is 15000 ft³. Enter your answer in the box.
A dumpster
A dumpster is shaped like a rectangular prism. It has a width of 8 feet, a height of 5 feet, and a volume of 880 cubic feet. What is the length of the dumpster?
The pool
There is 210 l of water in the pool. If you know that the pool is 30% full, calculate how many liters of water will fit into it?
Edges of the cuboid
Find the length of the edges of the cuboid, which has the following dimensions: width is 0.4 m; the height is 5.8 dm and the block can hold 81.2 liters of fluid.
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.
Cylinder container
If the cylinder-shaped container is filled with water to a height of 5 dm, it contains 62.8 hectoliters of water. Calculate the diameter of the bottom of the container. Use the value π = 3.14.
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.
Mr. Gardener
Mr. Gardener wants to make wood for the balcony. Boxes. Each will have the shape of a perpendicular prism with a square base, the height is limited to 60 cm. Each container will be filled with soil by pouring the whole bag of substrate sold in a package w
Regular quadrilateral pyramid
Find the surface area of a regular quadrilateral pyramid if for its volume V and body height v and the base edge a applies: V = 2.8 m ^ 3, v = 2.1 m
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.
The solar
The solar heating tank has the shape of a rotating cylinder. When the tank is in a horizontal position, the water in the tank wets 4/5 each tank bases. If we place the tank in a vertical position, the water in the tank will reach up to 1.2 m. Calculate th
Top-open tank
The top-open tank has the shape of a truncated rotating cone, which stands on a smaller base. The tank's volume is 465 m³, the radii of the bases are 4 m and 3 m. Find the depth of the tank.
The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?

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