Ask question

Ask question

All categories

3 years ago

10

Samuel cut a cone from a piece of wood shaped as a cylinder. He measured the circumference of the base of the cylinder and found

that it measured 3πinches. The height of the cylindrical piece of wood was 6 inches. What is the approximate volume of Samuel's cone if it has the same base area and height as the cylinder?

1 answer:

patriot [66]3 years ago

5 0

Answer:

The approximate volume of the cone is 14 cube inches.

Step-by-step explanation:

Circumference of the base of the cylinder = 3π inches

Height of the cylindrical piece of wood = 6 inches

volume of a cone = $\frac{1}{3}$ $\pi$ $r^{2}$ h

But,

circumference = 2πr

3π = 2πr

r = $\frac{3}{2}$

= 1.5 inches

Radius of the base of the cylinder is 1.5 inches.

So that;

volume of cone = $\frac{1}{3}$ x $\frac{22}{7}$ x $(\frac{3}{2}) ^{2}$ x 6

= $\frac{1}{3}$ x $\frac{22}{7}$ x $\frac{9}{4}$ x 6

= 14.143

volume of cone = 14.143 cube inches

The approximate volume of the cone is 14 cube inches.

You might be interested in

Select the correct answer.

Veronika [31]

Answer:

B

Step-by-step explanation:

let y = 5x - 3

rearrange making x the subject

add 3 to both sides

5x = y + 3 ( divide both sides by 5 )

x = $\frac{y+3}{5}$

change y back into terms of x, hence

$f^{-1}$ (x) = $\frac{x+3}{5}$ → B

4 0

3 years ago

Two ice cream shops in the mall sell sundaes. Let x equal the number of scoops of ice cream. Larry's ice cream shops price is re

Gnesinka [82]

Answer:

The answer is: The two shops never charge the same price for sundaes with the same number of scoops.

Step-by-step explanation:

6 0

3 years ago

Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1]

blagie [28]

$\green{\large\underline{\sf{Solution-}}}$

<u>Given expression is </u>

$\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }$

can be rewritten as

$\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} }$

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\$

And

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\$

So, using this identity, we

$\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }$

can be further rewritten as

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}$

$\rm \: = \: \dfrac{4}{25 - 1}$

$\rm \: = \: \dfrac{4}{24}$

$\rm \: = \: \dfrac{1}{6}$

<u>Hence, </u>

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}$

3 0

3 years ago

Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee A

kipiarov [429]

A

Step-by-step explanation:

ik trust me

8 0

3 years ago

Read 2 more answers

(10^4)^4 as an expression (simplified)

Verdich [7]

$(10^4)^4$

$10^8$

Therefore in simplified form $(10^4)^4$ is $10^8$

6 0

2 years ago