Volume and Surface Area Worksheet - Doghouse Maths

Students calculate the surface area of a compound 3-D shape by finding and summing the area of each unique face.

Students calculate the volume of a rectangular prism and a triangular prism that together form one compound shape.

Students apply a surface-area calculation to a real-world purchasing decision (how many containers of paint to buy).

Students explain, in writing, which formula they used to calculate each volume and why one face of the shape is excluded from the paint calculation.

Have students sketch the four unique faces on the grid before touching the calculation tables, since the hint in the file notes there are exactly four distinct face shapes to find.

Walk through the fractional edge length (one-half inch) as a class first, since it appears in the triangular roof section and could trip up students calculating area from the grid.

Use the coverage-rate question (200 square inches per paint container) as a checkpoint for whether students can move from a calculated total back to a real-world purchasing decision.

Surface area of compound 3-D shapes — students find and sum the area of each unique face of a combined rectangular-and-triangular prism.

Volume of rectangular and triangular prisms — students calculate and total the volume of each prism section separately.

Real-world measurement application — students convert a calculated surface area into a paint-container purchasing decision using a given coverage rate.