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Ivanshal [37]
3 years ago
13

Find the surface area and volume of the solid given the figure below

Mathematics
1 answer:
Zarrin [17]3 years ago
4 0

Answer:

Volume - 582.8848178 cm cubed

Step-by-step explanation:

Volume - to fine the volume start with the cone...

The formula is 1/3 pi r^2h

so for this problem it would be

1/3 * 3.14 * 26.01 * 11.2

so your answer would be...

305.061213 cm cubed

Your next step is to find the volume of the dome. to do that the formula is (4/3 pi r^3)/2

so for this problem it would be

(4/3 * 3.14 * 132.651)/2

so your answer would be...

277.8236048 cm cubed

Finally you add together those 2 volumes and get 582.8848178 cm cubed as your final answer.

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Step-by-step explanation:

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4 years ago
a person kicks a ball from the ground into the air with an initial upward velocity of 8 feet per second. what is the maximum hei
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Chech the picture below.

if the person kicked it from the ground, that means its initial height is 0.

it reaches its maximum height at the y-coordinate of its vertex, and it will hit the ground when y = 0, as you see in the picture.

\bf ~~~~~~\textit{initial velocity}&#10;\\\\&#10;\begin{array}{llll}&#10;~~~~~~\textit{in feet}&#10;\\\\&#10;h(t) = -16t^2+v_ot+h_o&#10;\end{array} &#10;\quad &#10;\begin{cases}&#10;v_o=\stackrel{8}{\textit{initial velocity of the object}}\\\\&#10;h_o=\stackrel{0}{\textit{initial height of the object}}\\\\&#10;h=\stackrel{}{\textit{height of the object at "t" seconds}}&#10;\end{cases}&#10;\\\\\\&#10;h(t)=-16t^2+8t+0

now let's find the y-coordinate of its vertex

\bf \textit{vertex of a vertical parabola, using coefficients}&#10;\\\\&#10;h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+8}t\stackrel{\stackrel{c}{\downarrow }}{+0}&#10;\qquad \qquad &#10;\left(-\cfrac{ b}{2 a}~~~~ ,~~~~  c-\cfrac{ b^2}{4 a}\right)&#10;\\\\\\&#10;\left(\qquad ,~~0-\cfrac{8^2}{4(-16)}  \right)\implies (\quad ,~0+1)\implies (\quad ,~1)

when will it hit the ground?

\bf \stackrel{h(t)}{0}=-16t^2+8t\implies 16t^2-8t=0\implies 8t(2t-1)=0&#10;\\\\\\&#10;8t=0\implies \stackrel{\textit{0 seconds when it took off first}}{t=0}&#10;\\\\\\&#10;2t-1=0\implies 2t=1\implies \stackrel{\textit{half a second later it  when it came back down}}{t=\cfrac{1}{2}}

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Answer: 15^{2} - 12^{2} \\= 81 = 9^{2}

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