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2 years ago

What is the surface area in square millimeters of the triangular pyramid?

Mathematics

1 answer:

alukav5142 [94]2 years ago

4 0

Answer:

31 mm² is the surface area.

Step-by-step explanation:

We know that:

Surface area of triangle = 3(1/2 x 4 x 4) + (1/2 x 4 x 3.5)

Work:

3(1/2 x 4 x 4) + (1/2 x 4 x 3.5) mm²
=> 3(2 x 4) + (2 x 3.5) mm²
=> 24 + 7 mm²
=> 31 mm²

Hence, 31 mm² is the surface area.

Hoped this helped.

$BrainiacUser1357$

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3 years ago

You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Aleksandr [31]

Answer:

Therefore the circumference of the circle is $=\frac{20\pi}{4+\pi}$

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

$\Rightarrow s=\frac{10-\pi r}{2}$

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

$A=\pi r^2+ (\frac{10-\pi r}{2})^2$

$\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2$

$\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}$

$\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25$

For maximum or minimum $\frac{dA}{dr}=0$

Differentiating with respect to r

$\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi$

Again differentiating with respect to r

$\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}$ > 0

For maximum or minimum

$\frac{dA}{dr}=0$

$\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0$

$\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}$

$\Rightarrow r=\frac{10}{4+\pi}$

$\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0$

Therefore at $r=\frac{10}{4+\pi}$ , A is minimum.

Therefore the circumference of the circle is

$=2 \pi \frac{10}{4+\pi}$

$=\frac{20\pi}{4+\pi}$

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3 years ago

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krek1111 [17]

Answer:

The answer is 6 wholes and 7/8ths.

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3 years ago

Find the area of a quarter circle with the radius of 6cm

Ronch [10]

Answer:

28.27cm³

Step-by-step explanation:

Area of a circle:

$A=\pi r^2$

First, find the area of a full circle with this given radius:

$\rightarrow A=(3.14159)(6)^2\\\rightarrow A=(3.14159)(36)\\\rightarrow A=113.09734\\$

Now, to find the radius of a quarter circle with the same radius, just divide by 4:

$\rightarrow A = \frac{113.09734}{4}\\\rightarrow A = 28.27433$

The radius of the quarter circle is about 28.27cm³

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2 years ago