We have been given that Wally wants to determine the height of a statue that casts a 164-inch shadow by comparing it to his own height and shadow length. Wally is 68 inches tall, casts a shadow that is 41 inches in length.

We will use proportions to solve for the height of the statue because proportions state that ratio between two proportional quantities is same.

$\frac{\text{Height of statue}}{\text{Shadow of statue}}=\frac{\text{Height of Wally}}{\text{Shadow of Wally}}$

Upon substituting our given values in above equation, we will get:

$\frac{\text{Height of statue}}{\text{164 cm}}=\frac{\text{68 inch}}{\text{41 inch}}$

$\frac{\text{Height of statue}}{\text{164 cm}}\times \text{164 cm}=\frac{\text{68 inch}}{\text{41 inch}}\times \text{164 cm}$

$\text{Height of statue}=\frac{\text{68 inch}}{1}\times 4$

$\text{Height of statue}=272\text{ inches}$

Therefore, the height of the statue is 272 inches.

5 0

2 years ago

The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.

Ber [7]

Answer:

Part 1) The volume of the object is $32\pi\ cm^{3}$ or $100.48\ cm^{3}$

Part 2) see the procedure

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

Part 1) What is the volume, in cubic centimeters, of the object?

we know that

The volume of the object is equal to the volume of the cylinder plus the volume of the cone

Find the volume of the cone

The volume of the cone is equal to

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

we have

$r=4/2=2\ cm$ -----> the radius is half the diameter

$h=3\ cm$

substitute the values

$V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}$

Find the volume of the cylinder

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=4/2=2\ cm$ -----> the radius is half the diameter

$h=(10-3)=7\ cm$

substitute the values

$V=\pi (2^{2})(7)=28\pi\ cm^{3}$

Part 2) Then explain how you found the volume of the total shape

The volume of the total shape is equal to the volume of the cylinder plus the volume of the cone

$4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3}$ ------> exact value

Find the approximate value of the volume

assume

$\pi=3.14$

$32(3.14)=100.48\ cm^{3}$

7 0

2 years ago

Read 2 more answers

There are 9 students in a class: 7 boys and 2girls.

AleksAgata [21]

Answer:

The probability is either 2 but mostly 3 boys.

Step-by-step explanation:

8 0

3 years ago

Solve each system by graphing. If the solution is not unique, identify the system as “inconsistent” or “dependent”

lapo4ka [179]

Answer:

therefore the solution of the system of equations is (x,y) = (4,2)

the solution is unique and therefore the the system is neither "inconsistent" nor "dependent"

Step-by-step explanation:

i) x + 2 = 6 $\Rightarrow$ x = 4

ii) x - y = 2 $\Rightarrow$ 4 - y = 2 , therefore y = 4 - 2 , therefore y = 2

iii) therefore the solution of the system of equations is (x,y) = (4,2)

iv) the solution is unique and therefore the the system is neither "inconsistent" nor "dependent"

6 0

3 years ago