Question

The composite figure is made up of a cone and a half sphere. The radius of the half sphere is 6 cm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth.
A half sphere and cylinder. Both have a radius of 6 centimeters. The cone has a height of 12 centimeters.


Recall the formulas V = one-third B h and V = four-thirds pi r cubed
188.40 cubic centimeters
489.84 cubic centimeters
904.32 cubic centimeters
1,356.48 cubic centimeters

Answer 1

Given:

Radius of half sphere and cone = 6 cm

Height of cone = 12 cm

To find:

The volume of composite figure that is made up of a cone and a half sphere.

Solution:

Volume of half sphere is:

$V_1=\dfrac{2}{3}\pi r^3$

Where r is the radius of the half sphere.

Putting $\pi =3.14, r=6$, we get

$V_1=\dfrac{2}{3}(3.14)(6)^3$

$V_1=\dfrac{6.28}{3}(216)$

$V_1=452.16$

Volume of a cone is:

$V_2=\pi r^2h$

Where r is the radius and h is the height of the cone.

Putting $\pi =3.14, r=6, h=12$, we get

$V_2=(3.14)(6)^2(12)$

$V_2=(3.14)(36)(12)$

$V_2=1356.48$

Volume of the composite figure is:

$V=V_1+V_2$

$V=452.16+1356.48$

$V=1808.64$

Therefore, the volume of a composite figure is 1808.64 cubic centimetres.

Note: All options are incorrect.