## Volume tutorial: what is volume; calculate / find volume of

x sin – 1 = 0 A: The equation 2cos2x-sinx-1=0 must be solved.question answerQ: A trough is 10 feet long and 2 feet wide at the top. It has isosceles triangles with altitude on its sides… A: Provided a trough length of l = 10 feet,
What is the first term of the sequence if the first term is 3?
A: To see the solution, please click here. respond to a question Q: Determine CA’s critical points: To see the solution, please click here. Set up the (triple) integral that describes the volume enclosed by the cone 2 +y? and the sphere in question answerQ: 8) A: Given the solid enclosed by the cone z=x2+y2 and the sphere x2+y2+z2=18, find the solid enclosed by the cone z=x2+y2. question answerQ: Using linear differential equations, solve the given equation. A: Using the equation y’ = x – 2y cot 2x,

## Volume – rectangular prisms

The cylindrical containers for rolled oats (dry oatmeal) have a diameter of 5 inches and a height of 9\$frac12\$ inches. These containers are delivered in boxes to grocery stores. Six rolled oats containers are included in each shipping box. The shipping company is attempting to decide the package dimensions that would use the least amount of cardboard when shipping the rolled oats containers. They are only considering rectangular prism boxes because they are easier to stack.
Students should consider various ways to arrange the cylindrical containers in a rectangular frame. Throughout the procedure, students should keep in mind that although some configurations appear to be different, they all result in the same volume box. Furthermore, students should realize (through debate and/or questioning) that the thickness of a cardboard box is extremely thin and has no bearing on the calculations.
Students can create the dimensions of the boxes and measure the different surface areas based on the various setups. Students can do so by building on their geometry work from previous grades. Students will use this information to measure the region of all six faces and then add them together. This project should teach students that each face has an identically sized equivalent, which will assist in the creation of the rectangular prism’s surface area formula. Furthermore, there is an opportunity to explore how the volume of two boxes can be the same despite the fact that their surface areas are different.

### Finding volume of irregular figures.

A box (plural: boxes) is a rectangular prism or container used for storing or transporting its contents. A box can be any size, from the tiniest (such as a matchbox) to the largest (such as a large appliance), and can be used for a range of purposes, from practical to decorative.
Boxes may be made of a range of materials that are usually durable, such as wood and metal, as well as non-durable materials like corrugated fiberboard and paperboard. Shipping containers are typically made of corrugated metal boxes.
Boxes are usually rectangular in shape with a rectangular cross-section, but they can also be square, elongated, circular, or oval; they can also have sloped or domed top surfaces or vertical sides, and they are not necessarily rendered square.
Flaps, doors, or a different lid may be used to lock and close boxes. Adhesives, tapes, or more decorative or elaborately functional devices, such as a catch, clasp, or lock, may be used to hold them locked.

### Grade 5 math #11.6, how many unit cubes

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