What is the volume of a rectangular prism with a length of 2x, a width of x−2, and a height of x + 2?
2 answers:
<h3><u>Answer:</u></h3>
- 2x³ - 8x is the volume of a rectangular prism.
- Volume: L x B x H
- => (2x) × (x - 2)(x + 2)
- => (2x) × (x² - 4)
- => 2x(x² - 4)
- => 2x³ - 8x units³ [According to DMAS rule]
Therefore, 2x³ - 8x units³ is the volume of a rectangular prism.
Hoped this helped.
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Consider the figure attached.
Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.
Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.