# MA.912.G.7.5 Volume, Lateral Area & Surface Area of Solids

## Trig & Discrete Math

Section 12-2; 830-837
Section 12-3; 838-846
Section 12-4; 847-854
Section 12-5; 857-863
Section 12-6; 864-871

## What You Need To Know...

Lateral area, surface area, and volume of solids.

1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
2. Items may use properties of congruent and similar solids, chords, tangents, and radii.
3. Items may be set in either mathematical or real-world contexts.
4. Items may refer to right prisms, right-circular cylinders, spheres, right pyramids, right-circular cones, and/or composites of these solids.

## Example One

Abraham works at the Delicious Cake Factory and packages cakes in cardboard containers shaped like right circular cylinders with hemispheres on top, as shown in the diagram below.

Abraham wants to wrap the cake containers completely in colored plastic wrap and needs to know how much wrap he will need.  What is the total exterior surface area of the container?

1.   90π  square inches
2. 115π square inches
3. 190π square inches
4. 308π  square inches

## Example Two

At a garage sale, Jason bought an aquarium shaped like a truncated cube.  A truncated cube can be made by slicing a cube with a plane perpendicular to the base of the cube and removing the resulting triangular prism, as shown in the cube diagram below.

What is the capacity, in cubic inches, of this truncated cube aquarium?