Hello!
The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure?
Use 3.14 to approximate π .
Enter your answer in the box. in.³
Data: (Cylinder)
h (height) = 7 in
r (radius) = 2.5 in (The diameter is 5 being twice the radius)
Adopting: \(\pi \approx 3.14\)
V (volume) = ?
Solving: (Cylinder volume)
\(V = \pi *r^2*h\)
\(V = 3.14 *2.5^2*7\)
\(V = 3.14*6.25*7\)
\(V = 137.375 \to \boxed{V_{cylinder} \approx 137.38\:in^3}\)
Note: Now, let's find the volume of a hemisphere.
Data: (hemisphere volume)
V (volume) = ?
r (radius) = 2.5 in (The diameter is 5 being twice the radius)
Adopting: \(\pi \approx 3.14\)
If: We know that the volume of a sphere is \(V = 4* \pi * \dfrac{r^3}{3}\) , but we have a hemisphere, so the formula will be half the volume of the hemisphere \(V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}\)
Formula: (Volume of the hemisphere)
\(V = 2* \pi * \dfrac{r^3}{3}\)
Solving:
\(V = 2* \pi * \dfrac{r^3}{3}\)
\(V = 2*3.14 * \dfrac{2.5^3}{3}\)
\(V = 2*3.14 * \dfrac{15.625}{3}\)
\(V = \dfrac{98.125}{3}\)
\(\boxed{ V_{hemisphere} \approx 32.70\:in^3}\)
Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)
Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 137.38 in³ + 32.70 in³
\(Volume\:of\:the\:figure =170.08 \to \boxed{\boxed{\boxed{Volume\:of\:the\:figure = 170\:in^3}}}\end{array}}\qquad\quad\checkmark\)
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I Hope this helps, greetings ... Dexteright02! =)
