The volume of wood in a tree varies jointly as the height of the tree and the
square of the distance around the tree trunk. If the volume of wood is 15.84 cubic
feet when the height is 22 feet and the distance around the trunk is 3 feet, what is
the volume of wood obtained from a tree that is 32 feet tall having a measurement
of 4 feet around the trunk?



please help :))

Answer:

The volume is 40.96 cubic feet

Step-by-step explanation:

Given

[tex]V\ \alpha\ h * d^2[/tex]

Where

[tex]V = Volume\\ h = height\\ d = distance[/tex]

[tex]V = 15.84ft^3; h =22ft; d = 3ft[/tex]

Required

The volume when h = 32 and d = 4

[tex]V\ \alpha\ h * d^2[/tex]

Express as an equation

[tex]V = khd^2[/tex]

Where k is the constant of variation.

Make k the subject

[tex]k = \frac{V}{hd^2}[/tex]

Substitute [tex]V = 15.84ft^3; h =22ft; d = 3ft[/tex]

[tex]k = \frac{15.84}{22 * 3^2}[/tex]

[tex]k = \frac{15.84}{22 * 9}[/tex]

[tex]k = \frac{15.84}{198}[/tex]

[tex]k = 0.08[/tex]

To solve for V when h = 32 and d = 4, we have:

[tex]V = khd^2[/tex]

[tex]V = 0.08 * 32 * 4^2[/tex]

[tex]V = 0.08 * 32 * 16[/tex]

[tex]V = 40.96[/tex]

The volume is 40.96 cubic feet

The volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is [tex]40.96 \: \rm ft^3[/tex]

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For this case, we have:
V = volume of the wood varying jointly as height of the tree and square of the distance around the trunk.

Let we take:

V will of course increase as r or h increases, and as it varies jointly, thus:

[tex]V \propto h r^2[/tex]

Let  the constant of proportionality be 'k', then:

[tex]V = kr^2h[/tex] (in cubic foot)

For case 1, it was specified that V = 15.84 cubic foot when r = 3 ft and h = 22 ft,

Putting these values gives us:

[tex]15.84 = k(3)^2(22)\\\\k = \dfrac{15.84}{198} = 0.08[/tex]

Thus, we have:

[tex]\rm V = 0.08r^2 h \: \rm ft^3[/tex]

Assuming second wood was also obtained from same kind of tree, we get the volume of the wood for h = 32 and r = 4 feet as:

[tex]V = 0.08 (4)^2 (32) = 40.96 \: \rm ft^3[/tex]

Thus, the volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is [tex]40.96 \: \rm ft^3[/tex]

Learn more about proportionality here:

https://brainly.com/question/13082482

She mixes nuts, raisins and oats in the ratio 3:2:5 by weight. Babajan uses 60 grams of nuts. Work out the weight of raisins she uses to make the breakfast cereal

For every 2 hours, approximately $1,186 worth of product is sold to consumers. How much money will the company for an entire month (30 days)?

70×2+20×30+19
are you okk guys❤​

6 pounds of sugar for $3 how much per pound

8.82 is 21% of what number?

I need the surface area again plz

What is the area of this green rectangle? | 7 in. 3 in.​

Select the correct answer from each drop menu. A functions with the domain {2,3,4} has a specific range. Determine the function and its range. The function with the domain {2,3,4} is, and it's range is?​

Can someone tel me which ones i need to put? I need to put 2.

A ship takes 5 hours to sail 75 kilometrs. What is its
speed?​

Can someone explain how to do this

2. Julio has 1/6 pound of candy. He puts the candy
into 4 bags. Write an expression that represents the
fraction.

SOLVE

270.6 is 16 1/2% OF WHAT NUMBER?

WILL GIVE BRAINLIST




X
X
X
X
X
X
X

Which statement is true about

please help asap!!

i need more chars here but please do help me

Find the area of the composite figure.
9 ft
4 ft
6 ft

What is the slope of the line shown below?

(9, 1) and (-3, -7

please help me I've been asking for this question for a while and I keep getting those spam messages please help me 15pts
How would you go about finding the confidence interval of say 90% or 95% for any given distribution scenario?​

20 POINTS HELP!!
What value of x and y make the polygon below a parallelogram

what is the surface area

7th grade math

The sales tax on an item is 6.5%. The total cost of the item is the price, p, plus the tax. Which expression represents the total cost?
A. 0.935p B. p + 1.065p C. 1.065p D. p + 6.5p

DF and GI are parallel lines.

Which angles are alternate interior angles?

Which expression is equivalent to the following complex fraction?
CO (
이고
X X
2
X-
2x
글
2x-2
X
12x
x-1



44 minutes left please help !!!!!!

can someone help me with this thanks

Write 3 1/9 as an improper fraction.

I need help with this question please

Find the measure of major arc QPN.
M
0
coll
IN

Help me with this question

A recipe calls for 3 cups of sugar for every 5 cups of water. How many cups of sugar are needed for 25 cups of water?

What is the solution to Three-fourths a greater-than negative 16?
a greater-than negative 21 and one-third
a less-than negative 21 and one-third
a greater-than 21 and one-third
a less-than 21 and one-third