Ask question

Ask question

All categories

3 years ago

11

Prism A is similar to Prism B. The ratio of the surface area of Prism A to Prism B is 81:4. Find the volume ratio of Prism A to

Prism B.

1 answer:

Damm [24]3 years ago

8 0

Answer:

The volume ratio of Prism A to Prism B is $\frac{729}{8}$

Step-by-step explanation:

Step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> scale factor

x/y----> ratio of the surface area of Prism A to Prism B

so

$z^{2}=\frac{x}{y}$

we have

$\frac{x}{y}=\frac{81}{4}$

substitute

$z^{2}=\frac{81}{4}$

$z=\frac{9}{2}$

step 3

Find the volume ratio of Prism A to Prism B.

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> scale factor

x/y----> volume ratio of Prism A to Prism B

so

$z^{3}=\frac{x}{y}$

we have

$z=\frac{9}{2}$

substitute

$(\frac{9}{2})^{3}=\frac{x}{y}$

$(\frac{729}{8})=\frac{x}{y}$

You might be interested in

2-[6÷2+{6×1/2+(7/2-3/2)}]

professor190 [17]

Answer:

-6

Step-by-step explanation:

2 - [6 ÷ 2 + {6 × 1/2 + (7/2 - 3/2)}] =

Follow the correct order of operations.

Do one step at a time and copy everything else each time, so you don't lose track of any operation.

= 2 - [6 ÷ 2 + {6 × 1/2 + 4/2}]

= 2 - [6 ÷ 2 + {6 × 1/2 + 2}]

= 2 - [6 ÷ 2 + {3 + 2}]

= 2 - [6 ÷ 2 + 5]

= 2 - [3 + 5]

= 2 - 8

= -6

5 0

3 years ago

Read 2 more answers

10 squared divided by 2c -b + 3a<br><br> A = 1/3<br> B= 9<br> C = 5

Svet_ta [14]

Answer:

50

Step-by-step explanation:

Figure out all variables

100/(2x5= 10)-9+(3x.33=1)

100/10-9+1

100/2

50

8 0

3 years ago

-2 (x + 3z) + 4x - 3y + 2z

andriy [413]

Answer:

-2 (x + 3z) + 4x - 3y + 2z

-2x-6x+4x-3y+2z

2x-4z-3y

hope it helps...

have a nice day!

6 0

3 years ago

Read 2 more answers

Genrish500 [490]

Given

$a\sqrt{x+b}+c=d$

we have

$\sqrt{x+b}=\dfrac{d-c}{a}$

Squaring both sides, we have

$x+b=\dfrac{(d-c)^2}{a^2}$

And finally

$x=\dfrac{(d-c)^2}{a^2}-b$

Note that, when we square both sides, we have to assume that

$\dfrac{d-c}{a}>0$

because we're assuming that this fraction equals a square root, which is positive.

So, if that fraction is positive you'll actually have roots: choose

$a=1,\ b=0,\ c=2,\ d=6$

and you'll have

$\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16$

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

$a=1,\ b=0,\ c=10,\ d=4$

and you'll have

$\sqrt{x}+10=4 \iff \sqrt{x}=-6$

Squaring both sides (and here's the mistake!!) you'd have

$x=36$

which is not a solution for the equation, if we plug it in we have

$\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4$

Which is clearly false

7 0

3 years ago

A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as

topjm [15]

Answer:

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.

Step-by-step explanation:

By definition of rectangular prism, we get the respective formulas for the volumes of the community swimming pool and the wadling pool, respectively:

Community swimming pool

$V_{c} = l\cdot w\cdot h (1)$

Wading pool

$V_{w} = \left(\frac{1}{2}\cdot l \right)\cdot \left(\frac{1}{2}\cdot h\right)\cdot w (2)$

Where:

l – Length of the swimming pool, measured in feet.

h – Depth of the swimming pool, measured in feet.

w – Width of the swimming pool, measured in feet.

$V_{c}$ – Volume of the community swimming pool, measured in cubic feet.

$V_{w}$ – Volume of the wading swimming pool, measured in cubic feet.

The ratio of the volume of the community swimming pool to the volume of the wadling pool is:

$\frac{V_{c}}{V_{w}} = \frac{l\cdot w \cdot h}{\left(\frac{1}{2}\cdot l \right)\cdot \left(\frac{1}{2}\cdot h\right)\cdot w} (3)$

$\frac{V_{c}}{V_{w}} = \frac{1}{\frac{1}{4} }$

$\frac{V_{c}}{V_{w}} = 4$

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.

8 0

2 years ago

Read 2 more answers