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3 years ago

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What is the volume, in cubic feet, of a cone that has a base area of π / 4 square feet and a height of 3 feet?

1 answer:

rewona [7]3 years ago

8 0

$The\ volume\ of\ a\ cone:V=\frac{1}{3}B\cdot H\\\\B=\frac{\pi}{4}ft;\ H=3ft\\\\therefore\\\\V=\frac{1}{3}\cdot\frac{\pi}{4}\cdot3=\boxed{\frac{\pi}{4}\ (ft^2)=\frac{1}{4}\pi\ (ft^2)}$

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Answer:

First option is the correct choice.

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

Please help!! MathsWatch, Surd Expressions, Clip 207c

dexar [7]

Answer:

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Step-by-step explanation:

see the attached figure with letters to better understand the problem

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a ----> the height of rectangle in mm

b ---> the base of rectangle in mm

step 1

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substitute

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step 2

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$a=FB+CG+GH$ ---> by segment addition postulate

substitute the given values

$a=3+CG+3\\a=6+CG$

Find the length sides CG

Applying the Pythagorean Theorem

$BG^2=BC^2+CG^2$

substitute the given values

$6^2=3^2+CG^2$

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Find the area of rectangle

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3 years ago

Find the area of the parallelogram with vertices:________.

marin [14]

Answer:

97.98

Step-by-step explanation:

The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;

Area of the parallelogram = |PQ×PS|

PQ = Q-P and PS = S-P

Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)

PQ = (4,-5,3) - (0,0,0)

PQ = (4,-5,3)

Also, PS = S-P

PS = (8,-12,4)-(0,0,0)

PS = (8,-12,4)

Taking the cross product of both vectors i.e PQ×PS

(4,5,-3)×(8,-12,4)

PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k

PQ×PS = -16i - 40j -88k

|PQ×PS| = √(-16)²+(-40)²+(-88)²

|PQ×PS| = √256+1600+7744

|PQ×PS| = √9600

|PQ×PS| ≈ 97.98

Hence the area of the parallelogram is 97.98

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3 years ago