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2 years ago

What is the exact volume of the cone

Mathematics

1 answer:

Travka [436]2 years ago

5 0

Answer:

V = $\frac{400}{3}$ $\pi$

Step-by-step explanation:

Volume of a cone is:

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

Substitute values given:

$V = \pi (5^{2} )(\frac{16}{3})$

$V = \pi (25)(\frac{16}{3} )$

V = $\pi \frac{400}{3}$

V = $\frac{400}{3}$ $\pi$

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Step-by-step explanation:

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3 years ago

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3 years ago

Select the simplification that accurately explains the following statement.

lutik1710 [3]

Answer:

Option (b) is correct.

$(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}=2^{1}=2$

Step-by-step explanation:

Given: $(2^\frac{1}{4} )^4$

We have too choose the correct simplification for the given statement.

Consider $(2^\frac{1}{4} )^4$

Using property of exponents, $(a^m)^n=a^m\times a^m\times a^m\times ....\times (n\ times)$

We have,

$(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}$

Again applying property of exponents $a^m\times a^m=a^{n+m}$

We have,

$(2^\frac{1}{4} )^4=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}$

Simplify, we have,

$(2^\frac{1}{4} )^4=2^{\frac{4}{4}}$

we get,

$(2^\frac{1}{4} )^4=2^{1}=2$

Thus, $(2^\frac{1}{4} )^4=2$

Option (b) is correct.

8 0

3 years ago

Read 2 more answers

What is the value of 6/x + 2x2, when x = 3?

aliina [53]

Replace x = 3 into <span>6/x + 2x^2

</span>6/x + 2x^2

=6/3 + 2 (3)^2
= 2 + 2(9)
= 2 + 18
= 20

3 0

3 years ago