Ask question

Ask question

All categories

2 years ago

12

Given a cube with a volume of 36 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?

2 answers:

LUCKY_DIMON [66]2 years ago

5 0

Hope you know that formula for volume of a cube is area of base time height
and volume of a square pyramid is area of base time height divide 3
- so in this your exercise case we know that area of cube is 36 cm^3 what is area of base time height
- so this mean that the volume of a square pyramide what can fit perfectly inside the cube will be equal 36/3 = 12 cm^3

stiv31 [10]2 years ago

3 0

Answer:

$\text{The volume of square pyramid is}12cm^3$

Step-by-step explanation:

Given a cube with a volume of 36 cubic centimeter. we have to find the volume of square pyramid that can fit perfectly inside the cube.

As the pyramid base is same as the side of cube

$\text{Volume of cube is }a^3$

$\text{Volume of square pyramid is=}\frac{a^3}{3}$ (∵a=h)

i.e the volume of square pyramid is one-third of the volume of cube.

∴ $\text{Volume of square pyramid is=}\frac{1}{3}\times\text{Volume of square pyramid}$

$=\frac{36}{3}=12cm^3$

Hence, $\text{the volume of square pyramid is}12cm^3$

You might be interested in

5x - 2 = 10 - X<br> Please help

finlep [7]

Answer:

x = 2

Step-by-step explanation:

5x - 2 = 10 - x

<em>Add x to both sides</em>

6x - 2 = 10

<em>Add 2 to both sides</em>

6x = 12

<em>Divide both sides by 6</em>

x = 2

3 0

2 years ago

Find y when x= -3 for y=2/3 x

marusya05 [52]

Answer:

y = - 2

Step-by-step explanation:

$y = \frac{2}{3} x \\ \\ plug \: x = - 3 \\ \\ y = \frac{2}{ \cancel3} \times ( \cancel{ - 3}) \: \: \red{ \bold{- 1}}\\ \\ y = 2( - 1) \\ \\ y = - 2$

7 0

2 years ago

Solve<br><img src="https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7Bp%7D%20%2B%20%5Cdfrac%7B1%7D%7Bq%7D%20%2B%20%5Cdfrac%7B1%7D

Nostrana [21]

Answer:

$\displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}$

Step-by-step explanation:

we would like to solve the following equation for x:

$\displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x}$

to do so isolate $\frac{1}{x}$ to right hand side and change its sign which yields:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x}$

simplify Substraction:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)}$

get rid of only x:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)}$

simplify addition of the left hand side:

$\displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)}$

divide both sides by q+p Which yields:

$\displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)}$

cross multiplication:

$\displaystyle x(p + q + x) = - pq$

distribute:

$\displaystyle xp + xq + {x}^{2} = - pq$

isolate -pq to the left hand side and change its sign:

$\displaystyle xp + xq + {x}^{2} + pq = 0$

rearrange it to standard form:

$\displaystyle {x}^{2} + xp + xq + pq = 0$

now notice we end up with a <u>quadratic</u><u> equation</u> therefore to solve so we can consider <u>factoring</u><u> </u><u>method</u><u> </u><u> </u>to use so

factor out x:

$\displaystyle x( {x}^{} + p ) + xq + pq = 0$

factor out q:

$\displaystyle x( {x}^{} + p ) +q (x + p)= 0$

group:

$\displaystyle ( {x}^{} + p ) (x + q)= 0$

by <em>Zero</em><em> product</em><em> </em><em>property</em> we obtain:

$\displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}$

cancel out p from the first equation and q from the second equation which yields:

$\displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}$

and we are done!

3 0

2 years ago

ILL GIVE BRAINLEST !!!!

VikaD [51]

Here ya go enjoy and I’m sorry if this isn’t what your looking for

4 0

2 years ago

There is 1 inch of snow on the ground when it begins to snow 0.75 inch per hour. Which linear equation represents the total dept

aleksandrvk [35]

Y=0.75x+1 is the answer

3 0

3 years ago