Question

Can you help solve this please 50 points for all questions

Answer 1

9) Volume of the cone: $9152 mm^3$

10) New volume of the cone: $339 mm^3$

11) The volume of the cone shrinks by a factor of $3^3=27$

12) Volume of the composite  figure: $15 ft^3$

Step-by-step explanation:

9)

The volume of a cone is given by the equation

$V=\frac{1}{3}\pi r^2 h$

where

$\pi r^2$ is the area of the base, where

r is the radius of the cone

h is the height of the cone

For the cone in this problem, we have:

r = 18 mm (radius)

h = 27 mm (height)

Therefore, the volume of this cone is

$V=\frac{1}{3}\pi (18)^2 (27)=9152 mm^3$

10)

In this second exercise, the radius and the height of the cone are divided by 3. Therefore we have:

$r'=\frac{r}{3}=\frac{18}{3}=6 mm$ is the new radius of the cone

$h'=\frac{27}{3}=9 mm$ is the new height of the cone

Therefore, the new volume of the cone is

$V=\frac{1}{3}\pi r'^2 h'$

And substituting, we find

$V=\frac{1}{3}\pi (6)^2 (9)=339 mm^3$

11)

We can understand what happened to the volume of the cone after dividing its dimensions by 3 by calculating the ratio of the original volume to the new volume:

$\frac{V}{V'}=\frac{9152}{339}=27$

This means that the new volume of the cone is 27 times smaller than the original volume.

We see that this "factor of shrinking" corresponds to the total factor of shrinking ofits dimensions, to the power of 3. In fact:

- Each the radius and the height of the cone has shrunk by a factor of 3

- However, the cone is a figure in 3  dimensions, so the total factor of shrinking of its volume is $3^3 = 27$

12)

The composite figure consists of a squared pyramid + a parallelepiped.

The volume of the square pyramid is given by:

$V_1 = \frac{1}{3}Lwh$

where

L = 5 ft is the length of the base

w = 1 ft is the width of the base

h = 6 ft is the height of the pyramid

Substituting,

$V_1 = \frac{1}{3}(5)(1)(6)=10 ft^3$

The volume of the parallelepiped is given by

$V_2=Lwh$

where

L = 5 ft is the length of the base

w = 1 ft is the width of the base

h = 1 ft is the height

Substituting,

$V_2 = (5)(1)(1)=5 ft^3$

So, the total volume of the composite figure is

$V=V_1+V_2=10+5=15 ft^3$

Learn more about volume of solids

brainly.com/question/12497249

#LearnwithBrainly

Answer 2

Answer:

9) Volume of the cone: 9152 mm^3

10) New volume of the cone: 339 mm^3

11) The volume of the cone shrinks by a factor of 3^3=27

12) Volume of the composite  figure: 15 ft^3

Step-by-step explanation: