MATHEMATICS HIGH SCHOOL

Cone A has a height of 3 meters and a radius of 2 meters. Cone B has the same radius, but the height is 6 meters. Calculate the volume of each cone. Which conclusion is correct?A) The volume of cone A is twice the volume of cone B.
Eliminate
B) The volume of cone B is twice the volume of cone A.
C) The volume of cone B is 4 times the volume of cone A.
D) The volume of cone B is three times the volume of cone A.

Answers

Answer 1

Answer: V=(1/3)hpir^2

Avol is (1/3)3pi2^2=4pi m^3

Bvol is (1/3)6pi2^2=2pi4=8pi m^3

B is twice vol A

answer is B

Answer 2

Answer:

Answer:

Step-by-step explanation:

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Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?0.8 ft

1.6 ft

9.8 ft

19.6 ft

Approximately, how long does it take until the soccer ball hits the ground again?

0.6 sec

0.8 sec

1.6 secs

2.8 secs

Answers

Answer:

Maximum height=9.8 ft and Time taken by soccer ball will be 0.8 secs

Step-by-step explanation:

Since, the ball kicked will take the motion of projectile, therefore using the equation: h(t)= $at^(2) +vt+d$ , where h(t) is the height of the soccer ball, a is the acceleration whose value is -16 ft/sec^2 and v= 35 feet and d is the starting height which is equal to zero.

Therefore, h(t)= $at^(2) +vt+d$ (1)

Differentiating this equation with respect to t,

$h^(')(t)$ = $2at+v$

$0$ = $2(-16)t+25$

$32t$ = $25$

$t= 0.781sec$

Substituting the value of t in equation (1),

$h(t)=-16(0.781)^(2) +25(0.781)$

= $(-16)(0.609)+19.525$

= $9.766$

≈9.8ft

Hence, option C is correct.

Now, In order to determine the time taken until the soccer ball hits the ground, we take the equation:

$h(t)= at^(2) +vt+d$

Since, when the ball hits the ground, the height will become equal to zero, therefore we have, h(t)=0

Now, $h(t)= at^(2) +vt+d$

$0= -32.174t^(2) +25t$

$0=t(-32.174t+25)$

Then, one solution is t=0 and the other is: $0=-32.174t+25$

$32t=25$

$t=(25)/(32.174)$

$t=0.777 sec$

$t$ ≈ $0.8 sec$

Hence, option B is correct.

Answer:

9.8 ft for the maximum height

1.6 sec for the time it’ll take for the ball to hit the ground again

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Answers

Hello,

w=width
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