Draw a diagram to represent the problem. Then solve.

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

Illusion [34]

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.

5 0

2 years ago

The top of a round table with a diameter of 5.5 feet is painted white. how many square feet are painted

Firlakuza [10]

The formula for area of a circle is:
A=(pi)r^2
If diameter is 5.5, divide by 2 to find radius is 2.75. 2.75^2 is 7.5625 then multiplied by 3.14 (pi) is 23.746.
Depending on how you round, about 23.7 square feet were painted.

5 0

2 years ago

PLS HELP ME

lianna [129]

Answer: Percentage increase: 57%

Percent increase if the airline charges an additional 50: 14.5% or 15%

Depends if your teacher wants more accurate results with the decimal, or rounded up with 15.

Step-by-step explanation:

Ill explain in the comments bc for some reason its not letting me put it here

7 0

2 years ago

The triangle shown below is reflected across the y-axis.

lys-0071 [83]

Answer:

yo need more photos

Step-by-step explanation:

4 0

2 years ago

What is 0.216 (26 recurring) as a fraction?

ankoles [38]

216/1000

Simplify it by 2

Give me a thanks if it helps!!!

8 0

3 years ago

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