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3 years ago

Find the volume and total surface area of a regular tetrahedron whose measure of one edge is 10cm

2 answers:

7 0

The total surface area of a regular tetrahedron is calculated through the equation,
SA = (sqrt 3) x a²
Substituting the known value,
SA = (sqrt 3) x (10 cm)² = 173.20 cm²
Its volume is obtained by,
V = ((sqrt 2)/ 12) x a³
V = ((sqrt 2) / 12) x (10 cm)³ = 117.85 cm³
Thus, its surface area and volume are 173.20 cm² and 117.85 cm³, respectively.

Diano4ka-milaya [45]3 years ago

3 0

For a tetrahedron, the total surface area is expressed as:
SA = √3 x a²
Substituting the given value,
SA = √3 x (10 cm)² = 173.20 cm²

The volume is expressed as,
V = (√2/ 12) x a³

Substituting the given values,
V = (√2 / 12) x (10 cm)³ = 117.85 cm³

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Consider the function V=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and V being the volume of an

Andrej [43]

Answer:

The maximum volume of the open box is 24.26 cm³

Step-by-step explanation:

The volume of the box is given as $V=g(x)$ , where $g(x)=x(6-2x)(8-2x)$ and $0\le x\le3$ .

Expand the function to obtain:

$g(x)=4x^3-28x^2+48x$

Differentiate wrt x to obtain:

$g'(x)=12x^2-56x+48$

To find the point where the maximum value occurs, we solve

$g'(x)=0$

$\implies 12x^2-56x+48=0$

$\implies x=1.13,x=3.54$

Discard x=3.54 because it is not within the given domain.

Apply the second derivative test to confirm the maximum critical point.

$g''(x)=24x-56$ , $g''(1.13)=24(1.13)-56=-28.88\:$

This means the maximum volume occurs at $x=1.13$ .

Substitute $x=1.13$ into $g(x)=x(6-2x)(8-2x)$ to get the maximum volume.

$g(1.13)=1.13(6-2\times1.13)(8-2\times1.13)=24.26$

The maximum volume of the open box is 24.26 cm³

See attachment for graph.

6 0

3 years ago

the volume of a cone is 36π cubic units. What is the volume of a cylinder that has the same base area and the same height?

ExtremeBDS [4]

V_cone = 1/3 pi * r^2 * h
V_cylinder = pi*r^2*h

If you multiply the cone's volume by 3 then you get the cylinder's volume. They become the same formula
3 V_cone = pi r^2 h
Since the cone's volume is 36pi They cylinder's volume is 3*36pi = 108 pi

6 0

3 years ago

Calculate the unit price of the following item:

Vikki [24]

10 lol that’s the answer.

7 0

3 years ago

Find the value of x. 101 x +29

iVinArrow [24]

Answer:

x = 50

Step-by-step explanation: