Q. 3TB - Calculus

Question

Setting up and solving a word problem involving volume: A specialty glass fask has a bulb-shaped bottom half and a cylindrical top half. The bull consists of a sphere with a radius of 10 centimeters whose top and bottom are truncated by 2 centimeters. The cylindrical tube has a radius just large enough to connect to the bulb and is 7 centimeters tall. Find the volume of the fask.

Step-by-Step Solution

Answer

a

Step 1: Compute sphere volume

The bulb is a sphere with radius 10 cm: \( V_{\text{sphere}} = \frac{4}{3}\pi(10)^3 = \frac{4000\pi}{3} \) cm\(^3\).

Step 2: Compute cylinder volume

The cylindrical top has the appropriate radius and height. Calculate \( V_{\text{cyl}} = \pi r^2 h \).

Step 3: Total volume

Add the volumes of the hemisphere (half of sphere) and cylinder portions as specified.