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2 years ago

A rectangular prism has a length of 4m, a height of 11m, and a width of 17m. What is its volume, in cubic m?

Mathematics

2 answers:

givi [52]2 years ago

8 0

Answer:

748m³

Step-by-step explanation:

Hello!

The volume of a rectangular prism is determined by the formula $l * w * h$ . To find the volume is to find how much space the object takes up in 3D. The formula is used to find the area of the base ( $l * w\\$ ), or the space taken on a 2D plane and multiplied by the height to give it 3 Dimensions.

Breakdown of $l * w * h$ :

$l$ is length
$w$ is width
$h$ is height

Find the Volume:

Use the formula and plug in values into the formula.

V = l * w * h
V = 4 * 17 * 11
748

Th units of length are m, and volume is the units cubed, so the units are m³.

The volume is 748m³

antoniya [11.8K]2 years ago

3 0

Answer:

748

Step-by-step explanation: V= W*H*L

17*11*4= 748m^3

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A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

Area of circle

Gre4nikov [31]

Answer:

1. area

2. circle

3. equilateral

4. length

5. perimeter

6. polygon

7. regular polygon

8. trapezoid

9. legs

10. area of a circle

11. hexagon

12. octagon

13. inscribed polygon

14. apothem

15. composite figure

Step-by-step explanation:

4 0

3 years ago

What is the solution of |-1 + x| = 5

nataly862011 [7]

Answer:

6, -4

Step-by-step explanation:

abs(-1+x)=5

-1+x=5 and -1+x=-5

-------------------------

-1+x=5

x=5-(-1)=5+1=6

-------------------

-1+x=-5

x=-5-(-1)=-5+1=-4

4 0

3 years ago

Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They

stellarik [79]

Formula for compound interest is

Interest = Amount - Principal

Interest = $P(1+r)^{t}$ - P

Where r = rate in percent

t = time in years

For Jaina,

P = $300

r= 7%

t = 3 yrs

So, Interest = $300(1+0.07)^{3}$ - 300

For Tomas

P = $400

r= 4%

t = 3 yrs

So, Interest = $400(1+0.04)^{3}$ - 400

So pair of equations for Jaina and Tomas are

Interest = $300(1+0.07)^{3}$ - 300

Interest = $400(1+0.04)^{3}$ - 400

5 0

3 years ago

Read 2 more answers

A house painter was told by his boss to purchase enough paint to cover 75 square feet to finish a project. The house painter hap

Rama09 [41]

It must be noted that the area of the square is calculated through the equation,
A = s²
where A is area and s is the measure of one side of the square.
To determine the measure of one side of the square, we simply have to get the square root of the area,
s = √A
Substituting the known value,
s = √75 ft² = 5√3 ft ≈ 8.66 cm
Thus, the answer to this question is approximately 8.66 cm.

7 0

3 years ago

Read 2 more answers