Surface Areas And Volumes

The correct answer is (B) : 19 : 45
∵ s1 + s2 = k
76x² + 3πr² = k
∴ 152x + 6πr = 0
∴ =
Now
V = + πr³
∴ = 120x² . + 2πr² = 0
⇒ 120x² . ( ) + 2πr² = 0
⇒ 120 =
⇒ = =

Step 1: Define the inequalities.
The region is bounded by the following inequalities: The points of intersection between the curves are: - and where intersects , - and where intersects .
Step 2: Set up the integral.
We need to calculate the area between the curves using the following integral expression: Step 3: Compute the first integral.
First, compute the integral for the region from to where the upper curve is : Evaluating this: Thus, the integral becomes: Step 4: Compute the second integral.
Next, compute the integral for the region from to where the curve is : Step 5: Combine the results.
Now combine the results from both integrals: Simplifying this expression: Final Answer: 20.