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2 years ago

A cone has a volume of about 28 cubic inches. Which are possible dimensions for the cone?

1 answer:

8 0

The formula for the volume, V of a cone is V = (1/3)*π*(radius)^2 * height.

So, as you see you have two variables, radius and height, which means that there are different combinations of radius and height that lead to the same volume.

That implies that your questions is missing some information.

I searched for it and found that the question has a list of answer choices. This is the list:

a) radius 6 inches, height 3 inches

b) diameter 6 inches, height 3 inches

c) diameter 4 inches, height 6 inches

d) diameter 6 inches, height 6 inches

Now you can probe those options to see which leads to an approximate volume of 28 cubic inches.

a) radius 6 in, height 3 in

=> V = (1/3)*3.14*(6in)^2 * 3in = 113.04 in^3 => not possible

b) diameter 6 in, height 3 inc

diameter 6 in => radius 3 in

=> V = (1/3)*3.14*(3in)^2 * 3in = 28.26 in^3 => this is the answer

The other options lead to values far from 28 in^3.

Answer: diameter 6 inches, height 3 inches.

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At the very beginning, when

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2 years ago

A bag of trail mix weighs 1.625 pounds round 1.625 to the nearest hundredths

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2 years ago

Which expression is equivalent to x Superscript negative five-thirds? StartFraction 1 Over RootIndex 5 StartRoot x cubed EndRoot

Anastasy [175]

Option B : $\frac{1}{\sqrt[3]{x^{5} } }$ is the expression equivalent to $x^{-\frac{5}{3}$

Explanation:

The given expression is $x^{-\frac{5}{3}$

Rewriting the expression $x^{-\frac{5}{3}$ using the exponent rule, $a^{-b}=\frac{1}{a^{b}}$

Hence, we get,

$\frac{1}{x^{\frac{5}{3} } }$

Simplifying, we get,

$\frac{1}{\left(x^{5}\right)^{\frac{1}{3}}}$

Applying the rule, $a^{\frac{1}{n}}=\sqrt[n]{a}$

Thus, we have,

$\frac{1}{\sqrt[3]{x^{5} } }$

Now, we shall determine from the options that which expression is equivalent to $x^{-\frac{5}{3}$

Option A: $\frac{1}{\sqrt[5]{x^{3} } }$

The expression $\frac{1}{\sqrt[5]{x^{3} } }$ is not equivalent to simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $\frac{1}{\sqrt[5]{x^{3} } }$ is not equivalent to $x^{-\frac{5}{3}$

Hence, Option A is not the correct answer.

Option B: $\frac{1}{\sqrt[3]{x^{5} } }$

The expression $\frac{1}{\sqrt[3]{x^{5} } }$ is equivalent to the simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $\frac{1}{\sqrt[3]{x^{5} } }$ is equivalent to $x^{-\frac{5}{3}$

Hence, Option B is the correct answer.

Option C: $-\sqrt[3]{x^5}$

The expression $-\sqrt[3]{x^5}$ is not equivalent to the simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $-\sqrt[3]{x^5}$ is not equivalent to $x^{-\frac{5}{3}$

Hence, Option C is not the correct answer.

Option D: $-\sqrt[5]{x^3}$

The expression $-\sqrt[5]{x^3}$ is not equivalent to the simplified expression $\frac{1}{\sqrt[3]{x^{5} } }$

Thus, the expression $-\sqrt[5]{x^3}$ is not equivalent to $x^{-\frac{5}{3}$

Hence, Option D is not the correct answer.

4 0

2 years ago

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