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1 year ago

What is the volume of a cone with the diameter 12 CM in height 4 cm

Mathematics

1 answer:

Romashka [77]1 year ago

8 0

The formula for the volume of a cone is

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

to find the radius divide the diameter by 2

$\begin{gathered} r=\frac{D}{2} \\ r=\frac{12}{2} \\ r=6 \end{gathered}$

replace all data in the formula

$\begin{gathered} V=\pi\cdot(6^2)\cdot\frac{4}{3} \\ V=\pi\cdot36\cdot\frac{4}{3} \\ V=(48\pi)cm^3^{} \end{gathered}$

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

One way to solve the system is to _____________ a variable.

Ivahew [28]

One way to solve the system is to <u>substitute</u> a variable.

<u>Explanation:</u>

One approach to solve an equation is by substitution of one variable. Right now, a condition for one factor, at that point substitute that arrangement in the other condition, and explain. All value(s) of the variable(s) that fulfills a condition, disparity, arrangement of conditions, or arrangement of imbalances.

The technique for tackling "by substitution" works by settling one of the conditions (you pick which one) for one of the factors (you pick which one), and afterward stopping this go into the other condition, "subbing" for the picked variable and fathoming for the other. At that point you back-explain for the principal variable.

8 0

3 years ago

Read 2 more answers

Match the algebraic expression to the real life scenario

Anarel [89]

The Correct mathes are :

1. x² - 4

2. 4x

3. x/5

4. 2x + 3

5. 3x - 1

6 0

3 years ago

Mitchell has $18 to spend. What is the greatest number of any one item he can buy?

NISA [10]

He can buy 6 water bottles that are $3 a piece.

3 0

3 years ago

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WILL GIVE BRAINLIST

borishaifa [10]

Answer:

option: C is correct.

Step-by-step explanation:

since, we are given a parent function f(x) as: f(x)=x.

We are asked to find what change will occur in the function when the parent function f(x) is replaced by f(9x).

let g(x) be the function formed by replacing f(x) with f(9x) i.e.

g(x)=f(9x)=9x.

clearly the slope of the function g(x)=f(9x) is 9. ( since on comparing the equation with the slope intercept form y=mx+c; where m is the slope of the line and c is the y- intercept).

whereas the slope of the function f(x)=x is 1.

Hence there is an increment of slope by a factor of 9.

Hence, option C is correct.

6 0

3 years ago