Mathematics, 26.07.2019 06:30 kelli151

Cavalieri's principle states that two solids with equal heights and base areas have equal volumes. a. true b. false

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Answer from: ZoomZoom44

So, the following statement is a TRUE statement.

Step-by-step explanation:

In geometry Cavalieri's priciple states that:

Cavalieri's Principle: If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.

Hence, the given statement:

Cavalieri's principle states that two solids with equal heights and base areas have equal volumes is a TRUE statement.

Answer from: KMyers

The answer is true.

Step-by-step explanation:

Given the statement about the Cavalieri's principle we have to tell is it true or false.

Cavalieri's principle states that:

If in two solids of equal height, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.

Very common example of Cavalleri's principle.

If two triangles are formed on base of equal length and are between same parallel lines i.e have same height, then the triangles are of equal area.

Hence, the given statement:

Cavalieri's principle states that two solids with equal heights and base areas have equal volumes is a TRUE statement.

Answer from: Quest

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

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