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Setler [38]
3 years ago
14

The radius r(t) of the base of a cone is increasing at a rate of 10 meters per second. The height h(t) of the cone is fixed at 6

meters. At a certain instant , the radius is 1 meter. What is the t 0 rate of change of the volume V(t) of the cone at that instant?
Mathematics
1 answer:
IceJOKER [234]3 years ago
8 0

Answer:

dV/dt = 40π

Step-by-step explanation:

We are told that The radius r(t) of the base of a cone is increasing at a rate of 10 meters per second. Thus;

dr/dt = 10 m

Height: h = 6 m

Volume of cone is given by the formula;

V = ⅓πr²h

dV/dr = ⅔πrh

We want to find the rate at which the volume is changing at radius of 1m.

Thus;

dV/dt = (dV/dr) × (dr/dt)

dV/dt = ⅔π(1 × 6) × (10)

dV/dt = 40π

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n200080 [17]
I think that first you need to understand what CPCTC is used for.

Let's start with the definition of congruent triangles.

Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.

A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.

Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.

Problem 1.

Statements                                        Reasons
1. Seg. AD perp. seg. BC               1. Given
2. <ADB & <ADC are right angles     2. Def. of perp. lines
3. <ADB is congr. <ADC                 3. All right angles are congruent
4. Seg. BD is congr. seg CD           4. Given
5. Seg. AD is congr. seg. AD        5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD           6. SAS
7. Seg. AB is congr. seg. AC        7. CPCTC

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3 years ago
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Answer:

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