A cone has a volume of 9π in3 and a diameter of 6 in. Wilson states that a cylinder with the same height and diameter has the same volume. Which statement explains whether or not Wilson is correct?

A. A cylinder in which h = 1 and d = 6 has a volume of 27π in3; therefore, Wilson is correct.
B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect.
C. A cylinder in which h = 1 and d = 6 has a volume of 9π in3; therefore, Wilson is incorrect.
D. A cylinder in which h = 3 and d = 6 has a volume of 9π in3; therefore, Wilson is correct.

B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect.

Step-by-step explanation:

step 1

Find the height of the cone

The volume of the cone is equal to

substitute the given values

simplify

step 2

Find the volume of the cylinder

The volume is equal to

substitute the given values

step 3

Compare the volumes

The volumes are not equal

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.