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spin [16.1K]
3 years ago
5

Which represents the volume of the cylinder, in cubic units? 120π 130π 300π 325π

Mathematics
2 answers:
IrinaVladis [17]3 years ago
5 0
Volume=(pi)(radius^2)(height)
Volume=(pi)(5^2)(12)
V=(pi)(25)(12)
V=(pi)(300)
Art [367]3 years ago
4 0

Answer:

The volume of the cylinder is equal to 300\pi\ units^{3})

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

V=\pi r^{2} h

we have

r=5\ units

h=12\ units

substitute the values

V=\pi (5^{2})(12)=300\pi\ units^{3}

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If you're using the app, try seeing this answer through your browser:  brainly.com/question/2762144

_______________


Let  \mathsf{\theta=cos^{-1}\!\left(\dfrac{4}{5}\right).}


\mathsf{0\le \theta\le\pi,}  because that is the range of the inverse cosine funcition.


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\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\&#10;\mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}


Square both sides and apply the fundamental trigonometric identity:

\mathsf{(5\,cos\,\theta)^2=4^2}\\\\&#10;\mathsf{5^2\,cos^2\,\theta=4^2}\\\\&#10;\mathsf{25\,cos^2\,\theta=16\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\&#10;\mathsf{25\cdot (1-sin^2\,\theta)=16}

\mathsf{25-25\,sin^2\,\theta=16}\\\\&#10;\mathsf{25-16=25\,sin^2\,\theta}\\\\&#10;\mathsf{9=25\,sin^2\,\theta}\\\\&#10;\mathsf{sin^2\,\theta=\dfrac{9}{25}}&#10;

\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{9}{25}}}\\\\\\&#10;\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{3^2}{5^2}}}\\\\\\&#10;\mathsf{sin\,\theta=\pm\,\dfrac{3}{5}}


But \mathsf{0\le \theta\le\pi,} which means \theta lies either in the 1st or the 2nd quadrant. So \mathsf{sin\,\theta} is a positive number:

\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\&#10;\therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}


I hope this helps. =)


Tags:  <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>

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