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2 years ago

The diagram shows a square pyramid over a cube. What is the volume of the entire figure?

Mathematics

1 answer:

TEA [102]2 years ago

3 0

Answer: 810

Step-by-step explanation:

first lets take down the information we were given,

height (h) of the pyramid should be 12 - 9 = 3

base (a) = 9

So we calculate the volume of a square pyramid

V = a²h/3

V = (9² × 3) / 3

v = (81 × 3) / 3

V = 81

now we calculate the volume of the cube using the formula

V = a³

V = 9³

V = 729

NOW to get the volume of the entire figure

we say

volume of square pyramid + volume of cube

81 + 729 = 810

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(−5)3x7(yz)4 / (3)2x2y8z2

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Answer:

$\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}$

Step-by-step explanation:

Given:

The expression to simplify is given as:

$\frac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}$

In order to simplify this, we have to use the law of indices.

1. $(ab)^m=a^mb^m$

So, $(yz)^4=y^4z^4$

Substitute this value in the above expression. This gives,

$=\dfrac{(-5)3x^7y^4z^4}{(3)2x^2y^8z^2}\\\\\\=\dfrac{-15x^7y^4z^4}{6x^2y^8z^2}......(-5\times 3=15\ and\ 3\times 2=6)$

Now, we use another law of indices.

2. $\frac{a^m}{a^n}=a^{m-n}$

So, $\frac{x^7}{x^2}=x^{7-2}=x^5,\frac{y^4}{y^8}=y^{4-8}=y^{-4}, \frac{z^4}{z^2}=z^{4-2}=z^2$

Substitute these values in the above expression. This gives,

$=\frac{-15}{6}\times x^5\times y^{-4}\times z^2\\\\=\frac{-5x^5y^{-4}z^2}{2}$

Finally, we further simplify it using the law $a^{-m}=\frac{1}{a^m}$

So, $y^{-4}=\frac{1}{y^4}$

Therefore, the given expression is simplified as:

$\dfrac{(-5)3x^7(yz)^4}{(3)2x^2y^8z^2}=\dfrac{-5x^5z^2}{2y^4}$

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Step-by-step explanation:

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