# An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is V cubic inches. This i v cubic inches less than the volume of the new chamber.

the original volume is lesser than the new volume by 242.47 in³

Step-by-step explanation:

Volume of a cone is;

V = ⅓πr²h

Where;

h is height

For the original chamber;

r = 5.7/2 = 2.85 inches

h = 12 inches

Volume of this original chamber is;

V_orig = ⅓ × π × 2.85² × 12

V_orig = 102.02 in³

In the new design, the chamber is scaled by a factor of 1.5.

Thus;

r_new = 2.85 × 1.5 = 4.275 inches

h_new = 12 × 1.5 = 18 inches

V_new = ⅓ × π × 4.275² × 18

V_new = 344.49 inch³

V_new - V_orig = 344.49 - 102.02 =

Thus, the original volume is lesser than the new volume by 242.47 in³

## Related Questions

6 students share 4 bagels equally. How many pieces does each person get? (p.s thanks to everyone who answers)

Solution:

we are given that

6 students share 4 bagels equally.

we have been asked to find that

How many pieces does each person get?

Here we will have to use the concept of division. Because we are dividing bagels among the students.

So To get the number of pieces each will get divide 6 by 4.

Number of Pieces for each boys

Hi!

You would get 1 and a half bagel for each person

6/4 = 1 1/2 or 1.5

A business student at Nowledge College must complete a total of 65 courses to graduate. The number of busi-ness courses must be greater than or equal to 23. The number of nonbusiness courses must be greater than or equal to 20. The average business course requires a textbook costing $60 and 120 hours of study. Non-business courses require a textbook costing$24 and 200 hours of study. The student has $3,000 to spend on books. ### Answers Based on the constraints and objective function that apply to the business student at Nowledge College, the set of linear equations are: • 60x + 24y ≤ 3,000 • x + y ≥ 65 • x ≥ 23 • y ≥ 20 ### What set of linear equations describe the constraints? Assume the number of business courses to be x and the number of nonbusiness courses to be y. The total cost of both need to be less than$3,000 so the inequality is:

60x + 24y ≤ 3,000.

Both courses need to be at least 65 if the student wants to graduate so:

x + y ≥ 65

Business courses should be equal to or more than 23 and nonbusiness courses should be greater than or equal to 20 so:

x ≥ 23

y ≥ 20

Find out more on linear equations at brainly.com/question/12788590.

69

Step-by-step explanation:

59

Step-by-step explanation:

If we convert from degrees into radians, we can use the formula

, where s is the arc length, r is the radius and θ is the angle in radians.

To convert from degrees to radians, we multiply by

So is our angle in radians, and we have the radius - we can now plug in these two values into our equation.

Step-by-step explanation:

length of arc= (arc angle/360) * 2πr

length= 140/360 *2*22/7*24

length=58.88 feet ~59 feet(approx)

Which fraction is bigger 7/36, or 4/9

4/9 is bigger

Step-by-step explanation:

For the 1st fraction, since 9 × 4 = 36,

4/9 = 4 × 4

9 × 4 = 16/36

Likewise, for the 2nd fraction, since 36 × 1 = 36,

7/36= 7 × 1

36 × 1 = 7/36

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16/36> 7/36 or 4/9 > 7/36

7/36 is bigger
7 goes into 36 5 times
and 4 goes in 9 only 4 times

Line p is parallel to line q. Parallel lines p and q are crossed by lines a and b to form 2 triangles. At parallel line p, angle 4 is formed by line b and angle 5 is formed by line a. Angle 6 is the third angle. At parallel line q, angle 3 is formed by line 3 and angle 2 is formed by line b. Angle 1 is the third angle. Which set of statements about the angles is true? Angle 1 is congruent to angle 6, angle 5 is congruent to angle 4, angle 3 is congruent to angle 2 Angle 2 is congruent to angle 4, angle 3 is congruent to angle 6, angle 1 is congruent to angle 5 Angle 3 is congruent to angle 6, angle 1 is congruent to angle 2, angle 5 is congruent to angle 4 Angle 6 is congruent to angle 1, angle 5 is congruent to angle 3, angle 4 is congruent to angle 2

a

Step-by-step explanation:

Step-by-step explanation:

What are 567 times 3