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3 years ago

What is the volume of the triangular pyramid shown, in cubic units?

Mathematics

2 answers:

ZanzabumX [31]3 years ago

8 0

Answer: 256

Step-by-step explanation: I just got done taking a test and it had this answer on there, and the corrct answer was 256

I have my way of solving this so 8 times 16 equals 128, times 128 by 2 then you have 256.

Hope this helps :D

tiny-mole [99]3 years ago

6 0

Answer:

256

Step-by-step explanation:

volume of the triangular pyramid = 1/3(area of triangle)height

1/3 (1/2bh)h

1/3(1/2x 8x16)12

4(4x16) = 4(64) = 256

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Find the volume of the prisms. Show work!

Fed [463]

1. Answer = About 1451.42 m³

First, we need to find the volume of the cube:
Formula: πr²h

Volume = π * 3² * 50 = 1413.72 m³
Second, we need to find the volume of the cone:
Formula: (πr²h)/3
Volume = π * 3² * 4 = 37.69 m³
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2. Answer = 960 m³

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1/2 * 8 * 12 = 48.
Second, we need to multiply the area of the base by the height to get the volume.
B * h = 48 * 20 = 960 m³.

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2 years ago

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3 years ago

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2 years ago

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The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

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3 years ago