How do you solve that

Kazeer [188]

The answers are $8^{3}$ and 8 · 8 · 8

Explanation:

The volume of a cube or space a cube occupies is calculated by multiplying the length, height, and width. Additionally, because in a cube all sides are equal in length, the formula for volume is V= $s^{3}$ . According to this, if the side length is 8 inches the volume can be represented as $V = 8^{3}$ or V= 8 · 8 · 8 because the symbol · represents multiplication. Also, this can be solved as V = 512 cubic inches. This makes the following options correct: $8^{3}$ and 8 · 8 · 8.

4 0

4 years ago

Question 9 of 10

creativ13 [48]

Answer:

the answer is D i believe

3 0

3 years ago

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

Kate walks half a mile to the library. how many yards does she walk?

Novosadov [1.4K]

880 yards.

Explanation:

In one mile, there are 1760 yards. To find half of that, divide 1760 by two.
1760 ÷ 2 = 880

5 0

4 years ago

Read 2 more answers

consider a wire 2 ft long cut into two pieces. one piece forms a circle with radius r and the other forms a square with side len

makkiz [27]

The formula for the radius r in terms of x . and for the maximum areas is x=2/ $\pi$ +4

Given that,

y forms a circle of radius r

y=2 $\pi$ r

r=y/2 $\pi$

(2-y)- forms Square Side x

(2-y) = 4x

x=(2-y)/4

Now Sum of Area's=Area of Square +Area of Circle

Sum = $\pi$ r² + x²

Substitute the r and x values in above equation,

A(y)= y²/4 $\pi$ +(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4 $\pi$ + 2(y-2)/16 =0

y/2 $\pi$ + (y-2)/8 =0

y = 2 $\pi$ / $\pi$ +4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/ $\pi$ +4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/ $\pi$ +4

Learn more about Area :

brainly.com/question/28642423

#SPJ4

4 0

2 years ago