1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sineoko [7]
2 years ago
14

A solid right pyramid has a square base. The length of the base edge is4 cm and the height of the pyramid is 3 cm period what is

the volume of the pyramid?

Mathematics
1 answer:
Illusion [34]2 years ago
5 0

Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume V of a solid pyramid can be given as:

\displaystyle V = \frac{1}{3} \cdot b \cdot h,

where

  • b is the area of the base of the pyramid, and
  • h is the height of the pyramid.

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be x cm.

  • At the vertice of this pyramid, x = 0 and the length of a side of the square is also 0.
  • At the base of this pyramid, x = 3 and the length of a side of the square is 4 cm.

As a result, the length of a side of the square will be

\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x.

The area of the square will be

\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}.

Integrate the area of the horizontal cross-section with respect to x

  • from the top of the pyramid, where x = 0,
  • to the base, where x = 3.

\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}.

In other words, the volume of this pyramid is 16 cubic centimeters.

You might be interested in
Which equation is equivalent to
Aleksandr [31]

Answer:

(4x^2 +9)(4x^2-9) =0

Step-by-step explanation:

16x^4 - 18 = 0

Rewriting

(4x^2)^2 - 9^2 =0

We notice that this is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(4x^2 -9)(4x^2+9) =0

5 0
2 years ago
Read 2 more answers
Which label on the cone below represents the height?<br> *<br> A<br> B<br> C<br> D
posledela

Answer:

The answer is B.

Step-by-step explanation:

Let us go through each of the points one by one:

The label A represents the radius of the base of the cone.

The label B represents the height of the cone.

The label C represents the origin of the base of the cone.

The label D represents the vertex of the cone (where the cone ends).  

So it is choice B that represents the height of the cone.

<em>P.S: it is tempting to pick label D to represent the height, but since label A already points to a line that is the height of the cone, we don't pick Label D.</em>

4 0
2 years ago
Read 2 more answers
Mickey said that 45.7654 rounded to the nearest thousandth is 45.765 and Nicole said that it was 45.766. Who is correct and why?
Nesterboy [21]

Answer:

Mickey

Step-by-step explanation:

Mickey is correct because if you look at the number 45.7654 whenever you round to the nearest thousandth it'll be 45.765

5 is the thousandth place so look to the right. If the number to the right is greater than 5 it'll round to 47.766 but since it's a four ti rounds down.

8 0
2 years ago
Read 2 more answers
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per
ValentinkaMS [17]

Answer:

3lbs

Step-by-step explanation:

8 0
3 years ago
mr. tyler has a total of $5,000 in savings account and in a mutual fund. If he has x dollars in the savings account, how much do
eduard
5000-x is the number of dollars in the mutual fund
6 0
2 years ago
Read 2 more answers
Other questions:
  • Adam Wants To tip the room service person 15 Percent Of The Food bill Of 163.56 How Much Should He Tip
    6·2 answers
  • there were 135 cars in a rally. Each driver paid a 25 dollar fee to participate in the rally.How much money did the drivers pay
    15·2 answers
  • Ax+ by = c <br><br> solve for y
    11·1 answer
  • Which polynomial, when added to the polynomial 5x^2-3x-9 is equivalent to: 18
    7·1 answer
  • A pyramid has a square base with side s. The height of the pyramid is 2/3 that of its side. What is the expression for the volum
    13·2 answers
  • If the volume of a cone is 757 units and the height of the cone is uits, what is the radius of the cone?
    7·1 answer
  • This one is also giving me a hard time
    11·1 answer
  • Decide if the expression is positive or negative. Explain in words how you know, please.
    5·1 answer
  • If a4a3 is divisible by 11, what is a?(a is a number)
    8·1 answer
  • Find the domain and range of y= square root of x minus 1​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!