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2 years ago

A cone has volume of 12\pi cubic inches. Its height is 4 inches. What is its radius?

Mathematics

1 answer:

asambeis [7]2 years ago

6 0

The radius of cone is 3 inches.

Step-by-step explanation:

Given,

Volume of cone = 12π cubic inches

Height of cone = 4 inches

Let,

r be the radius of cone.

Volume of cone = $\pi r^2\frac{h}{3}$

$\pi r^2\frac{4}{3}=12\pi$

Multiplying both sides by 3

$3*\pi r^2\frac{4}{3}=12\pi * 3\\4\pi r^2 =36\pi$

Dividing both sides by 4π

$\frac{4\pi r^2}{4\ pi}=\frac{36\pi }{4\pi }\\\\r^2=9$

Taking square root on both sides

$\sqrt{r^2}=\sqrt{9}\\r=3$

The radius of cone is 3 inches.

Keywords: volume, radius

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Of a triangle

arsen [322]

Complete question is attached.

Answer:

a) ED = 6.5 cm

b) BE = 14.4 cm

Step-by-step explanation:

From the triangle, we are given the following dimensions:

AB = 20 cm

BC = 5 cm

CD = 18 cm

AE = 26 cm

We are asked to find length of sides ED and BE.

a) Find length of ED.

From the triangle Let's use the equation:

$\frac{AB}{BC} = \frac{AE}{ED}$

Cross multiplying, we have:

AB * ED = AE * BC

From this equation, let's make ED subject of the formula.

$ED = \frac{AE * BC}{AB}$

Let's substitute figures,

$ED = \frac{26 * 5}{20}$

$ED = \frac{130}{20} = 6.5$

Therefore, length of ED is 6.5 cm.

b) To find length of BE, let's use the equation:

$\frac{AB}{AC} = \frac{BE}{CD}$

Cross multiplying, we have:

AB * CD = AC * BE

Let's make BE subject of the formula,

$BE = \frac{AB * CD}{AC}$

From the triangle, length AC = AB + BC.

AC = 20 + 5 = 25

Substituting figures, we have:

$BE = \frac{20 * 18}{25}$

$BE = \frac{360}{25} = 14.4$

Therefore, length Of BE is 14.4cm

7 0

2 years ago

Can someone help me answer

Ilya [14]

Answer: she should by 9 bottles of juice

Step-by-step explanation:

because there's 2 L per one bottle, 2L (X bottles) = 18L, X = 9

3 0

2 years ago

Read 2 more answers

Can someone please answer. There is a picture. It is only one question. Thank you so much!

omeli [17]

The last answer - hypothenuse

3 0

2 years ago

How to do 15 1/2 - 2 1/10 how to do it

lisov135 [29]

First, you need to make the fractions have the same denominator:

15 1/2 ---> 15 + (1/2 x 5) = 15 5/10

2 1/10 ---> 2 1/10

Then you need to subtract them from each other:

15 5/10

<u>- 2 1/10</u> (or) 15 5/10 - 2 1/10 = 13 4/10

13 4/10

This gets the answer: <u>13 4/10</u>

8 0

2 years ago

The vector v⃗ in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.

allsm [11]

The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis is: (0, -1/2, √3/2).

<h3>Vector</h3>

a. Vector (v)

Vector (v)=v (cos Ф, sin Ф)

V=1 while the counterclockwise angle that is measured from positive x=Ф=π/4

Hence:

Vector=3(cos π/4, sinπ/4)

Vector=(3/√2, 3√2)

b. Vector w:

Vector w=1(0, cos 2π/3, sin2π/3)

Vector w=(0, -1/2, √3/2)

Therefore the vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector ws: (0, -1/2, √3/2).

The complete question is:

Resolve the following vectors into components:

a. The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.

(b) The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis.

Learn more about vector here:brainly.com/question/25705666

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5 0

1 year ago