Question

Find the surface area and volume of the figure.

(Round to the nearest teeth as needed)

Answer 1

Volume;

Let's find the volume of the hemisphere above,

Formula for hemisphere volume:

V = 2/3πr

Where pi(π) is 22/7 or 3.14, and 'r' is the radius.

(extra info:) D/2 = radius

So, diameter in this case is 6,

6/2 = 3 is the radius.

Replace values:-

V = 2/3πr

V = 2/3 x 3.14(3)

V = 2/3 x 9.42

V = 18.84/3

V = 6.28 feet is the volume for the hemisphere.

Now the cylinder's volume,

Cylinder volume formula:

V = π
`r^(2)`h

Where pi(π) is 22/7 or 3.14, 'r' is the radius which is being squared, and 'h' is the height.

Replace values (we figured out radius is 3);

V = π
`r^(2)`h

V = 3.14(3^2) x 10

V = 3.14(9) x 10

V = 28.26 x 10

V = 282.6 feet is the volume of the cylinder.

Add our volumes:-

6.28 + 282.6

= 288.88 feet is our volume.

Surface area;

Now the surface area formula of the cylinder is:

SA = 2πrh(lateral area) + 2π
`r^(2)`(area of circle)

Replace values:

SA = 2πrh + 2π
`r^(2)`

SA = 2(3.14) x 10 + 2(3.14) x 3^2

SA = 6.28 x 10 + 6.28 x 9

SA = 62.8 + 56.52
SA = 119.32 is the surface area of the cylinder.

Now the surface area formula of the hemisphere;

SA = 3πr²

Replace values;

SA = 3πr²

SA = 3(3.14) x 3^2

SA = 9.42 x 9

SA = 84.78 is the surface area of the hemisphere.

Add the areas;

119.32 + 84.78

= 204.1 feet is the surface area.