All categories

3 years ago

Find the volume of a solid

Mathematics

1 answer:

fredd [130]3 years ago

4 0

Answer:Volume = Area of the base × height

Step-by-step explanation:

If the rectangular box were filled with 1 cm cubes, there would be:

6 × 2 cubes in the bottom layer

As there are 3 layers,

Volume = 36 cubic centimetres

Now note that the area of the box's base is given by:

Area = 12 square centimetres

From the above discussion, we can derive a formula for the volume of a rectangular box as follows:

You might be interested in

PLEASE HELP!!!!

Lunna [17]

NOTES:

Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:

if "a" is positive, then opens UP
if "a" is negative, then opens DOWN

Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:

the Axis Of Symmetry (x-value) is: x = $\frac{-b}{2a}$
y-value is found by plugging in the AOS for "x" in the equation

****************************************************************************************

1) y = x² + 11x + 24

a = +1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-11}{2(1)}$ = $-\frac{11}{2}$

y = $(-\frac{11}{2})^{2}$ + 11 $(-\frac{11}{2} )$ + 24 = $-\frac{25}{4}$

vertex $(-\frac{11}{2}$ , $-\frac{25}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)

******************************************************************************************

2) y = -x² - 6x - 8

a = -1 so the parabola opens DOWN

x = $\frac{-b}{2a}$ = $\frac{-(-6)}{2(-1)}$ = $\frac{6}{-2}$ = -3

y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1

vertex (-3, 1) is in Quadrant 2 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)

******************************************************************************************

3) y = x² - 2x + 3

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-(-2)}{2(1)}$ = $\frac{2}{2}$ = 1

y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2

vertex (1, 2) is in Quadrant 1 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). There are no x-intercepts

******************************************************************************************

4) y = x² + 4x + 4

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-4}{2(1)}$ = -2

y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0

vertex (-2, 0) is in Quadrant 2 and is on the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). The x-intercept is the vertex.

Compared to the other four graphs, this is most likely the equation for the rain gauge!

******************************************************************************************

5) y = 3x² + 21x + 30

a = +3 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-21}{2(3)}$ = $-\frac{7}{2}$

y = 3 $(-\frac{7}{2})^{2}$ + 21 $(-\frac{7}{2} )$ + 30 = $-\frac{27}{4}$

vertex $(-\frac{7}{2}$ , $-\frac{27}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)

*******************************************************************************************

4 0

3 years ago

Read 2 more answers

Can someone find the surface area please

lozanna [386]

To find the surface area of any object, the first step that you must do is find all shapes that are present in the object.

Here we have 2 triangles and 3 rectangles.

Knowing this, simply find the area of each shape.

Since the triangles are the same, one is facing up and the other down, they both would be 15.6 cm^2.

The rectangles would be 54 cm^2. as there are 3 ( 6 x 3 cm) ones.

Add the values up to have the surface area.

It’s 85.2 cm^2.

3 0

3 years ago

Read 2 more answers

HELP!! Simplify the expression 3y^2 • 4x^2y • 5x Using the laws of exponents. Show each step of your work.

JulsSmile [24]

3y^2 • 4x^2y • 5x = (3*4*5) * (y^2 * y) * (x^2*x) = 60 * y^3 * x^3 = 60 (xy)^3

where ((y^2 * y)) adding the powers in case of multiplication

and also for this: (x^2*x)

5 0

3 years ago

Instructions: The polygons in each pair are similar. Find the missing side length.

adoni [48]

Answer:

Step-by-step explanation:

25 = x

20 16

(25*16)/20 = 20

4 0

2 years ago

The multiplicative inverse of -7/8 is

suter [353]

7/8 is a answer of this question

3 0

3 years ago