Question

Solve the following problems:

1. A cylindrical container is 20 cm high and has a radius of 5 cm. what is its Volume? Useπ=3.14

2. A rectangular pyramid has a base of 24 cm by 14 cm and height of 15cm. what is its Volume?

3. what is the Volume of a square pyramid if its base measures 9 m and it's height measures 24 m?

4. A mug is 10 dm in height and 10 dm in diameter. what is the Volume of the cylindrical mug?

5. A Cylindrical can of milk has diameter of 14 cm and has a height of 20 cm. what is the capacity of the can?​

Answer 1

Answer:

Often, we first learn about volume using rectangular prisms (specifically right rectangular prisms), such as by building the prism out of cubes.

Note that any face of a rectangular prism could be its base, as long as we measure the height of the prism perpendicularly to that face.



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\begin{aligned} \text{Volume}_{\text{rectangular prism}}&=(\blueE{\text{Area}_{\text{rectangle}}})\cdot (\maroonD{\text{height}})\\\\ &=\left(\blueE{(\text{rectangle base})(\text{rectangle height})}\right)\cdot (\maroonD{\text{prism height}})\\\\ &=\blueE{lw}\maroonD{h} \end{aligned}Volumerectangular prism=(Arearectangle)⋅(height)=((rectangle base)(rectangle height))⋅(prism height)=lwh

Triangular prisms

A triangular prism has a base shaped like a triangle.



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\begin{aligned} \text{Volume}_{\text{triangular prism}}&=(\blueE{\text{Area}_{\text{triangle}}})\cdot (\maroonD{\text{height}})\\\\ &=\left(\blueE{\dfrac{1}{2}(\text{triangle base})(\text{triangle height})}\right)\cdot (\maroonD{\text{prism height}})\\\\ &=\blueE{\dfrac{1}{2}bh}\maroonD{\ell} \end{aligned}Volumetriangular prism=(Areatriangle)⋅(height)=(21(triangle base)(triangle height))⋅(prism height)=21bhℓ

Cylinders

A circular cylinder is a prism-like figure that has a base shaped like a circle.



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\begin{aligned} \text{Volume}_{\text{circular cylinder}}&=(\blueE{\text{Area}_{\text{circle}}})\cdot (\maroonD{\text{height}})\\\\ &=(\blueE{\pi \cdot (\text{radius})^2})\cdot (\maroonD{\text{height}})\\\\ &=\blueE{\pi r^2}\maroonD{h} \end{aligned}Volumecircular cylinder=(Areacircle)⋅(height)=(π⋅(radius)2)⋅(height)=πr2h

Oblique prisms

In oblique prisms, the bases are in parallel planes,

We still calculate the volume in exactly the same way because of Cavalieri's principle.

Which expression gives the volume of the oblique rectangular prism?



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