Question

The figure is made up of a hemisphere and a cylinder.

What is the volume of the figure?


Enter your answer in the box.

Answer 1

283 1/3 pi

The figure is made up of a hemisphere and a cylinder.

What is the exact volume of the figure?

Enter your answer in the box. 283 1/3 pi

I hope this helps

Answer 2

Data: (Cylinder)
h (height) = 8 cm
r (radius) = 5 cm
Adopting:
`\pi \approx 3.14`
V (volume) = ?

Solving:(Cylinder volume)

`V = h* \pi *r^2`

`V = 8*3.14*5^2`

`V = 8*3.14*25`

`\boxed{ V_(cylinder) = 628\:cm^3}`

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)
V (volume) = ?
r (radius) = 5 cm
Adopting:
`\pi \approx 3.14`

If: We know that the volume of a sphere is
`V = 4 * \pi * (r^3)/(3)`, but we have a hemisphere, so the formula will be half the volume of the hemisphere
`V = (1)/(2) * 4 * \pi * (r^3)/(3)`

Formula: (Volume of the hemisphere)

`V = (1)/(2) * 4 * \pi * (r^3)/(3)`

Solving:

`V = (1)/(2) * 4 * \pi * (r^3)/(3)`

`V = (1)/(2) * 4 * 3.14 * (5^3)/(3)`

`V = (1)/(2) * 4 * 3.14 * (125)/(3)`

`V = (1570)/(6)`

`\boxed{V_(hemisphere)\approx 261.6\:cm^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 = 628 cm³ + 261.6 cm³

`\boxed{\boxed{Volume\:of\:the\:figure = 1517.6\:cm^3}}\end{array}}\qquad\quad\checkmark`