What is the surface area, in cm^2 of the figure? please help with my homework:)

A cylinder has a height of 4 inches greater than the radius of its base. Find the radius and the height to the nearest inch if t

anastassius [24]

Answer:

$h=5in, r=1in$

Step-by-step explanation:

The volume of a cylinder is:

$V=\pi*r^2*h$

where $r$ is the radius and $h$ is the height.

The height is 4 inches greater that the radius, so:

$h=r+4in$

Substituting this in the formula for volume:

$V=\pi*r^2*(r+4)$

the volume is $V=5\pi in^3$

thus:

$5\pi in^3=\pi*r^2*(r+4in)$

Dividing everything between pi:

$5in^3=r^2*(r+4in)$

$5in^3=r^3*+4r^2$

We can see that the solution for this is $r=1in$

since $(1)^3*+4(1)^2=1+4=5$

We have the radius, now we find the height:

$h=r+4in=1in + 4in = 5in$

$h=5in, r=1in$

7 0

3 years ago

Read 2 more answers

What is the measure of the indicated central angle ?

kolezko [41]

Answer:

nrhrjsjsnnsbeheheuuwuwjebebbrrbrb

Step-by-step explanation:

bdbdbdhshsjajajksndbdhejwnab

5 0

3 years ago

8x^3+2x^2-8 estimate the relative maxima and relative minima

DIA [1.3K]

Compute the derivative:

$\dfrac{\mathrm d}{\mathrm dx}\bigg[8x^3+2x^2-8\bigg]=24x^2+4x$

Set equal to zero and find the critical points:

$24x^2+4x=4x(6x+1)=0\implies x=0,-\dfrac16$

Compute the second derivative at the critical points to determine concavity. If the second derivative is positive, the function is concave upward at that point, so the function attains a minimum at the critical point. If negative, the critical point is the site of a maximum.

$\dfrac{\mathrm d^2}{\mathrm dx^2}\bigg[8x^3+2x^2-8\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[24x^2+4x\bigg]=48x+4$

At $x=0$ , the second derivative takes on the value of $4$ , so the function is concave upward, so the function has a minimum there of $-8$ .

At $x=-\dfrac16$ , the second derivative is $-4$ , so the function is concave downward and has a maximum there of $-\dfrac{431}{54}$ .

6 0

3 years ago

A line on a coordinate plane passes through the point (2, -7) and has a slope of 0.75.

andrey2020 [161]

Answer:

Step-by-step Correct answer to the question This table gives a few (x, y)(x, y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane

6 0

3 years ago

What is the side length of the eectagkes

dedylja [7]

1. 5 in and 1/3 in: Area = 5/3 in^2

2. 5 in and 4/3 in: Area= 20/3 in^2

3. 5/2 in and 4/3 in: Area=10/3 in^2

4. 7/6 in and 6/7 in: Area = 1 in^2

Step-by-step explanation:

1. 5 in and 1/3 in

Here,

$Let\\l=5\\w=\frac{1}{3}\\Area=l*w\\=5*\frac{1}{3}\\=\frac{5}{3}\ in^2$

2. 5 in and 4/3 in

Here,

$l= 5\ in\\w=\frac{4}{3}\ in\\Area=l*w\\=5*\frac{4}{3}\\=\frac{20}{3}\ in^2$

3. 5/2 in and 4/3 in

$let\\l=\frac{5}{2}\\w=\frac{4}{3}\\Area= \frac{5}{2}*\frac{4}{3}\\=\frac{20}{6}=\frac{10}{3}\ in^2$

4. 7/6 in and 6/7 in

Let

$l=\frac{6}{7}\\w=\frac{7}{6}\\Area=l*w\\=\frac{6}{7}*\frac{7}{6}\\=1\ in^2$

Hence,

1. 5 in and 1/3 in: Area = 5/3 in^2

2. 5 in and 4/3 in: Area= 20/3 in^2

3. 5/2 in and 4/3 in: Area=10/3 in^2

4. 7/6 in and 6/7 in: Area = 1 in^2

Keywords: Rectangle, Area

Learn more about rectangles at:

#LearnwithBrainly

8 0

4 years ago