# The sum of the altitude and the base radius of a cylinder is #63 cm#. The radius is #4/5# as long as the altitude. Calculate the surface area volume of the cylinder?

Surface area of cylinder is

Assume pi=22/7#, hence surface area of cylinder given by

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Let's denote the altitude as (h) and the base radius as (r).

Given that the sum of the altitude and the base radius is (63) cm, we have the equation: [h + r = 63]

Also, the radius is (\frac{4}{5}) times the altitude, so: [r = \frac{4}{5}h]

Now, we can substitute the expression for (r) in terms of (h) into the first equation to solve for (h): [h + \frac{4}{5}h = 63] [1\frac{4}{5}h = 63] [9/5h = 63] [h = \frac{63 \times 5}{9}] [h = 35]

Now that we have found (h), we can find (r): [r = \frac{4}{5} \times 35] [r = 28]

With (h = 35) and (r = 28), we can now calculate the surface area and volume of the cylinder.

Surface Area: [A = 2\pi rh + 2\pi r^2]

[A = 2\pi \times 28 \times 35 + 2\pi \times 28^2]

[A = 1960\pi + 1568\pi]

[A = 3528\pi]

Volume: [V = \pi r^2h]

[V = \pi \times 28^2 \times 35]

[V = 27440\pi]

So, the surface area of the cylinder is (3528\pi) square cm and the volume is (27440\pi) cubic cm.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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