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Wewaii [24]
4 years ago
8

If the length of each side of a cube is doubled, is the surface area doubled? Use an example to support your answer

Mathematics
1 answer:
sashaice [31]4 years ago
4 0
If a = 6l^2 is the total area of the surface of a cube with sides l length and A = 6 (2l)^2 is that area with 2l sides, then we take the ratio A/a = 6 (2l)^2/(6 l^2) = (2l)^2/l^2 = 4l^2/l^2 = 4. So that A = 4a. And that explicitly shows that the area A with 2l for sides is 4 X a, where a is the area when l is the side length. 

<span>Using ratios to compare values of the same thing is the smart way to solve this kind of problem, because many of the values, like the 6 in both, cancel out. In fact, because we found that A/a = (2l/l)^2 we say in general that the area of a cube varies with the square of the length of its side.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!</span>
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Answer:

The area of rhombus PQRS is 120 m.

Step-by-step explanation:

Consider the rhombus PQRS.

All the sides of a rhombus are equal.

Hence, PQ = QR = RS = SP = 13 m

The diagonals PR and QS bisect each other.

Let the point at of intersection of the two diagonals be denoted by <em>X</em>.

Consider the triangle QXR.

QR = 13 m

XR = 12 m

The triangle QXR is a right angled triangle.

Using the Pythagorean theorem compute the length of QX as follows:

QR² = XR² + QX²

QX² = QR² - XR²

       = 13² - 12²

       = 25

 QX = √25

       = 5 m

The measure of the two diagonals are:

PR = 2 × XR = 2 × 12 = 24 m

QS = 2 × QX = 2 × 5 = 10 m

The area of a rhombus is:

\text{Area}=\frac{1}{2}\times d_{1}\times d_{2}

Compute the area of rhombus PQRS as follows:

\text{Area}=\frac{1}{2}\times PR\times QS

        =\frac{1}{2}\times 24\times 10\\\\=120

Thus, the area of rhombus PQRS is 120 m.

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Answer:

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Step-by-step explanation:

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