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3 years ago

5

Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm3, what is the v

olume of B?

2 answers:

Rashid [163]3 years ago

7 0

Answer:

The volume of cone is $6\pi\ cm^{3}.$

Step-by-step explanation:

Formula

$Volume\ of\ a\ cylinder = \pi r^{2}h$

$Volume\ of\ a\ cone = \pi\ r^{2}\frac{h}{3}$

Where r is the radius and h is the height .

As given

Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm³.

Thus

$Volume\ of\ cone = \frac{1}{3}\times Volume of cylinder$

$Volume\ of\ cone = \frac{18\pi }{3}$

$Volume\ of\ cone = 6\pi\ cm^{3}$

Therefore the volume of cone is $6\pi\ cm^{3}.$

Artemon [7]3 years ago

5 0

The volume of a cone is (1/3) that of its similar cylinder.
Thus the volume of the cone B would be: $6 \pi cm^{3}$

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A 9.85 m ladder is placed against a wall. The height to the top of the ladder is 5 m more than the distance between the wall and

Dafna1 [17]

Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

$Hypotenuse^2=Base^2+Perpendicular^2$

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

$(9.85)^2=x^2+(x+5)^2$

$97.0225=x^2+x^2+10x+25$

$0=2x^2+10x+25-97.0225$

$0=2x^2+10x-72.0225$

Here, $a=2, b=10,c=-72.0225$ . Using the quadratic formula, we get

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}$

$x=\dfrac{-10\pm \sqrt{676.18}}{4}$

Approximating the value, we get

$x=\dfrac{-10\pm 26}{4}$

$x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}$

$x=\dfrac{16}{4},\dfrac{-36}{4}$

$x=4,-9$

Distance cannot be negative so $x\neq -9.$

Now we have $x=4$

$x+5=4+5$

$x+5=9$

Therefore, the base is 4 m and the height is 9 m.

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3 years ago

Help me to prove the given below. Thank you in advance

sleet_krkn [62]

Answer:

Construct MO, where O is the midpoint of CG. (As shown in the attached figure)

(1) LM = MG //given, CM is the median to the hypotenuse

(2) CO = OG // construction

(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment

(4) MO // LC //triangle mid-segment theorem

(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)

(6) m∠LCO=90° //given, ΔLCG is a right triangle

(7) m∠MOG=90° //(5), (6), definition of congruent angles

(8) m∠MOC=180° – 90° = 90° // linear pair

(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles

(10) MO=MO //common side, reflexive property of equality

(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate

(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)

(13) MG= ½LG // Given, CM is the median to the hypotenuse

(15) MC = ½LG //(12) , (13), substitution

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3 years ago

Simplify (-2) ^2 + |-15| ÷ 3

mixas84 [53]

4+I-15I÷3
4+15÷3
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Vadim26 [7]

Answer:

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Step-by-step explanation:

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