Virginia SOL Math / Grade 7 / Measurement & Geometry

7.MG.1

Volume & Surface Area of Prisms and Cylinders

What you'll learn

  • Find the volume of rectangular prisms and cylinders
  • Find the surface area of rectangular prisms and cylinders
  • Solve problems in context involving volume and surface area

Words to know

Volume —
the amount of space inside a solid, measured in cubic units
Surface area —
the total area of all the faces or surfaces of a solid
Prism —
a solid with two parallel, congruent bases joined by rectangles
Cylinder —
a solid with two parallel, congruent circular bases
Base area —
the area of one base of a solid

Why it matters Volume tells us how much a box or tank holds, and surface area tells us how much material wraps around it, which matters for packing and building.

Worked examples

Model ItI do

Find the volume of a rectangular prism 5 cm by 3 cm by 4 cm.

Volume equals length times width times height: 5 times 3 times 4. First 5 times 3 = 15, then 15 times 4 = 60 cubic cm.

Try It TogetherWe do

Find the volume of a cylinder with radius 2 cm and height 10 cm. Use 3.14 for pi.

Volume equals pi times radius squared times height. Radius squared is 4, so 3.14 times 4 times 10 = 125.6 cubic cm.

Now YouYou do

Find the surface area of a cube with edges of 4 cm.

A cube has 6 equal square faces; find one face area, then multiply by 6. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find the volume of a rectangular prism 2 cm by 3 cm by 4 cm.

  2. 2.Find the base area of a cylinder with radius 2 cm. Use 3.14 for pi.

  3. 3.Find the volume of a cube with edges of 3 cm.

On Level

The core Quick Check from the book.

  1. 1.Find the volume of a prism 2 m by 6 m by 3 m.

  2. 2.Find the volume of a cube with edges of 5 cm.

  3. 3.Find the base area of a cylinder with radius 3 cm. Use 3.14 for pi.

  4. 4.Find the surface area of a prism with faces totaling 12, 12, 8, 8, 6, and 6 square cm.

  5. 5.Find the volume of a cylinder with base area 10 square cm and height 7 cm.

Challenge

Stretch your thinking.

  1. 1.Find the volume of a cylinder with radius 3 cm and height 10 cm. Use 3.14 for pi.

  2. 2.Find the surface area of a rectangular prism 5 cm by 4 cm by 2 cm.

  3. 3.A cylindrical tank has base area 15 square feet and height 8 feet. Find its volume.