All categories

3 years ago

‼️GEOMETRY‼️

Mathematics

1 answer:

ella [17]3 years ago

6 0

Answer:

A.) 1018 square inches

Step-by-step explanation:

The largest sphere will have a diameter equaling the length of the cube (see picture).

If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:

$SA=4\pi r^2$

For this formula, we need the radius of the sphere. Divide the diameter by 2:

$\frac{18}{2}=9$

The radius is 9 inches. Plug this into the equation:

$SA=4\pi *9^2$

Simplify the equation:

$SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87$

Round the result to the nearest whole number:

$1017.87$ → $1018$

The surface area is 1,018 inches².

:Done

Picture:

In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.

You might be interested in

Sin Z=0.6561 A 48 degrees B 41 degrees C 53 degrees D 0.01 degrees

serg [7]

The answer would be b

8 0

3 years ago

Match the expression on the left with the correct simplified expression on the right.

andriy [413]

Given: The expression below

$\begin{gathered} (\frac{(3x^3y^4)^3}{(3x^2y^2)^2})^2 \\ (\frac{(3x^4y^2)^4}{(3x^5y^2)^3})^2 \end{gathered}$

To Determine: The matching expression to the given expressions

Solution

Let us simplify each of the expressions using exponents rule

$\begin{gathered} Exponent-Rule1=(a^m)^n=a^{m\times n} \\ Exponent-Rule2=(\frac{a^m}{a^n})=a^{m-n} \end{gathered}$

Applying the exponent rule 1 above to the given expressions

$\begin{gathered} (3x^3y^4)^3=3^3x^{3\times3}y^{4\times3}=27x^9y^{12} \\ (3x^2y^2)^2=3^2x^{2\times2}y^{2\times2}=9x^4y^4 \end{gathered}$ $\begin{gathered} (3x^4y^2)^4=3^4x^{4\times4}y^{2\times4}=81x^{16}y^8 \\ (3x^5y^2)^3=3^3x^{5\times3}y^{2\times3}=27x^{15}y^6 \end{gathered}$

Applying the exponent rule 2

$\frac{(3x^{3}y^{4})^{3}}{(3x^{2}y^{2})^{2}}=\frac{27x^9y^{12}}{9x^4y^4}=\frac{27}{9}x^{9-4}y^{12-4}=3x^5y^8$ $\frac{(3x^{4}y^{2})^{4}}{(3x^{5}y^{2})^{3}}=\frac{81x^{16}y^8}{27x^{15}y^6}=\frac{81}{27}x^{16-15}y^{8-6}=3xy^2$

Let us not apply exponent rule 1 above

$(\frac{(3x^{3}y^{4})^{3}}{(3x^{2}y^{2})^{2}})^2=(3x^5y^8)^2=3^2x^{5\times2}y^{8\times2}=9x^{10}y^{16}$ $(\frac{(3x^{4}y^{2})^{4}}{(3x^{5}y^{2})^{3}})^2=(3xy^2)^2=3^2x^2y^{2\times2}=9x^2y^4$

Hence, the matching is as shown below

8 0

2 years ago

Plz help me :,( also show the work too /:

ZanzabumX [31]

Answer:

Surface Area for cube: 263 inches^3

Step-by-step explanation:

Formula: 2lw + 2lh + 2wh

2(6 1/2)(3) + 2(6 1/2)(7) + 2(3)(7) =

39 + 182 + 42 =

263 inches

Hope This Helps! :-)

6 0

4 years ago

Solve for x in the triangle

grigory [225]

Answer: 49
explanation: since the triangle is a right angle, that means it is 90 degrees, so if you subtract the 41 degrees from 90 you get 49.

7 0

3 years ago

Explain why y +1 = 1.2(x+2) and y-5= 1.2(x – 3) represent the same line, despite having

andrew11 [14]

Answer:

You can manipulate both equations into y = mx + b format and end up with the same result of y = 1.2x + 1.4

Step-by-step explanation:

y + 1 = 1.2(x + 2)

y = 1.2x + 2.4 - 1

y = 1.2x + 1.4

y - 5 = 1.2(x - 3)

y = 1.2x - 3.6 + 5

y = 1.2x + 1.4

So essentially, they're the same equation but in different forms.

6 0

3 years ago