Mathematics: All the edges of a cube are expanding at a rate of 4 in. per second. How fast is the volume changing when each edge is 10 in. long

The diagonal is 421.Step-by-step explanation:This is a difficult question. To find the diagonal, you need to find the base and the height of the square. After that, you need to make it a triangle, by using this equation; (A being area, B being base, and H being height) then find the length of the hypotenuse of the triangle, which I will do for you. The B and H = 416. Plug it into the equation now;Now that you have done that, we know that the area of our new triangle is 86,528.The diagonal is:...

All the edges of a cube are expanding at a rate of

Ответ:

lilly198o

16.03.2022

Mathematics

Given:

All the edges of a cube are expanding at a rate of 4 in. per second.

To find:

The rate of change in volume when each edge is 10 in. long.

Solution:

Let a be the edge of the cube.

According to the question, we get

$\dfrac{da}{dt}=4\text{ in./sec}$

$a=10\text{ in.}$

We know that, volume of a cube is

V=a^3

Differentiate with respect to t.

$\dfrac{dV}{dt}=\dfrac{d}{dt}a^3$

$\dfrac{dV}{dt}=(3a^2)\times \dfrac{da}{dt}$

Putting the given values, we get

$\dfrac{dV}{dt}=(3(10)^2)\times 4$

$\dfrac{dV}{dt}=3(100)\times 4$

$\dfrac{dV}{dt}=300\times 4$

$\dfrac{dV}{dt}=1200\text{ in}^3\text{/sec}$

Therefore, the rate of change in volume 1200 cubic inches per second.

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Ответ:

rozzy5132

13.05.2023

Mathematics

The diagonal is 421.

Step-by-step explanation:

This is a difficult question. To find the diagonal, you need to find the base and the height of the square. After that, you need to make it a triangle, by using this equation; $A=\frac{1}{2} BH$ (A being area, B being base, and H being height) then find the length of the hypotenuse of the triangle, which I will do for you.

32*13=416 The B and H = 416. Plug it into the equation now;

$A=\frac{1}{2}(416*416)\\\\\\A=\frac{1}{2} 173,056\\\\\\A=86,528$ Now that you have done that, we know that the area of our new triangle is 86,528.

The diagonal is: 421

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All the edges of a cube are expanding at a rate of 4 in. per second. How fast is the volume changing when each edge is 10 in. long

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