A gym is investigating which paper cups to use for its water fountain. Which best compares the volumes of cup A and cup B?

d) volume of A is half volume of B

Step-by-step explanation:

The question is incomplete without the diagram of the paper cups to be used for the water fountain.

Find attached the complete question which has the diagram that would be used to answer the question.

To determine the answer, let's check the options provided.

a) volume of A and B are equal

The shape is a cone.

Volume of cone = (1/3)(π × r^2 ×h)

For cone A:

Radius = r, height = 2r

Volume of A = (1/3)(π × r^2 × 2r)

Volume of A = (2/3)(π × r^3)

For cone B:

Radius = 2r, height = r

Volume of B = (1/3)(π × (2r)^2 × r)

= (1/3)(π ×4 ×r^2 ×r)

Volume of B = 4/3(π × r^3)

Volume of B = 2(2/3)(π × r^3)

Volume of B = 2×Volume of A

Therefore option A is wrong

b) volume of B is half volume of A

Option B is wrong

c) volume of B is 4 times volume of A

Option C is wrong

d) volume of A is half volume of B

Volume of B = 2×Volume of A

1/2(Volume of B)= Volume of A

Option D is correct

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.