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3 years ago

The square pyramid has a volume of 27 cubic inches. What is the value of X?

Mathematics

1 answer:

wolverine [178]3 years ago

5 0

Answer:

9 inches

Step-by-step explanation:

base is rectangular in shape

Side of base of square pyramid is X inches

height of square pyramid is 1/9 X

Volume of any pyramid is 1/3 *(area of base* height of pyramid)

area of base of square pyramid = Side of base * Side of base

as area of square is equal to side * side

area of base of square pyramid = x* x square inches = $x^2 sq.\ inches$

Volume of pyramid = 1/3 *(area of base* height of pyramid)

substituting given value of of volume of pyramid , height of pyramid and area of base calculated above we have

$27 = 1/3(x^2)*(1/9 x)\\\\27*3*9 = x^3\\729 = x^3\\x = \sqrt[3]{729} \\x = 9$

Therefor value of x is 9 inches.

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The area of a square is A and side is y. Express A in terms of y

kolezko [41]

Answer:

A = y^2

A = (y)(y) = y^2

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3 years ago

A decagon with points labeled a through j clockwise. point a is the top left point. if this regular decagon is rotated countercl

serg [7]

The e vertex of the decagon will be in the top position after rotating it counterclockwise by 3 times the smallest angle of rotation.

Which vertex will be in the top position of the regular decagon?

A regular decagon has 10 sides of equal lengths with points labeled 'a' through 'j' clockwise. It is given that the point a is the top-left point. Hence, the the vertex which is in the the top position currently is 'b'.

Now, the smallest angle of rotation will be the angle between the two sides of the decagon.

In the first rotation by the smallest angle in counterclockwise direction, point 'c' will come to the top position. In the second rotation by the smallest angle in counterclockwise direction, point 'd' point will become the top most vertex. Finally, after the third similar rotation, 'e' vertex will be in the top position of the decagon. (Refer the attached diagram)

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5 0

2 years ago

Read 2 more answers

Which statements about the cylinder are true? Select two

Rus_ich [418]

Answer:

The radius of the cylinder is (1/2)x units

The area of the cylinder’s base is (1/4)πx2 square units

The height of the cylinder is 4x units

Step-by-step explanation:

The complete question is

A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is (1/2)x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder’s base is (1/4)πx2 square units.

(4) The area of the cylinder’s base is (1/2)πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units

we know that

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=\frac{x}{2}\ units$ ----> the radius is half the diameter

$V=\pi x^{3}\ units^3$

substitute the given values in the formula of volume

$\pi x^3=\pi (\frac{x}{2})^{2}h$

solve for h

simplify

$x=(\frac{1}{4})h$

$h=4x\ units$

Verify each statement

(1) The radius of the cylinder is (1/2)x units

The statement is true

see the explanation

(2) The radius of the cylinder is 2x units.

The statement is false

Because, the radius of the cylinder is x/2 units

(3) The area of the cylinder’s base is (1/4)πx2 square units

The statement is true

Because, the area of the cylinder's base is equal to

$A=\pi r^{2}$

$r=\frac{x}{2}\ units$

substitute

$A=\pi (\frac{x}{2})^{2}$

$A=\frac{\pi x^2}{4}\ units^2$

(4) The area of the cylinder’s base is (1/2)πx2 square units.

The statement is false

Because, the area of the cylinder's base is equal to

$A=\frac{\pi x^2}{4}\ units^2$

see the part (3)

(5) The height of the cylinder is 2x units.

The statement is false

Because, the height of the cylinder is 4x units (see the explanation)

(6) The height of the cylinder is 4x units

The statement is true

see the explanation

7 0

3 years ago

If 36 units is 75% how much is 100%

hodyreva [135]

Answer:

48 units

Step-by-step explanation:

75%=36

or 3/4=36

then 1/4=12 and 4/4=48

8 0

3 years ago

Read 2 more answers

Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type the answer exactly in this f

WINSTONCH [101]

We can get the inverse function by first setting f(x) = y, solving for x, and after that switching y and x. So, let's solve for x:
$f(x)= \frac{1}{2}x+4$
$y= \frac{1}{2}x+4$
$2(y-4)=x$
$2x-4=y=f (x)^{-1}$

Then, just plug in 4 for x, and solve:
$2(4)-4= f (x)^{-1}$
$4=f (x)^{-1}$

There you have your answer.

4 0

3 years ago