# Calculus Exercises: Building Solids with Various Cross Sections

- Author:
- Tim Brzezinski

- Topic:
- Calculus, Geometry, Integral Calculus, Prism, Volume

## Note the dimensions of the Toblerone shown below.

The Toblerone candy bar shown is an example prism. By definition, what exactly makes a 3D solid a *prism*? Describe.

## The solid below has equilateral triangle cross sections parallel to the yAxis. Given the dimensions of the Toblerone shown above, construct an accurate model of it below.

## Create a solid whose base is a circle with radius 8 and has equilateral triangle sections parallel to the yAxis. (Cross sections shown here are equilateral triangles.)

## This solid has 45-45-90 triangle cross sections parallel to the yAxis (leg lies in base). Create a solid with a base that is similar to these cross sections so that its (base) area = 50.

Which of the following solids has a volume that can be expressed as a **single** definite integral and not the sum of one or more definite integrals? Check all that apply.