Unit 5 STAAR Review

Unit 5:

Surface Area & Volume

​Surface Area

Surface area is the area of the outside surface of a 3-dimensional shape.

• Lateral: All surfaces besides the bases (top & bottom)

• Total: All surfaces

PRISMS

• P = Perimeter of the base

• h = height of the prism (distance between the two bases)

• B = Area of the base

  • Triangular Prisms: B = 1/2bh (h is height of the triangle & b is the base or bottom of triangle)

  • Rectangular Prism: B = bh (b and h are the length and width of rectangle base)

CYLINDERS

• h = Height of the prism (distance between the two circle bases)

• r = radius of the base

• If given the diameter, divide by two to get the radius

• Surface Area is measured in units²

Fill in the Blanks

Multiple Choice

• S = (7+4+7) x 9

• S = (7+9+7) x 4

• S = (7x4x7) x 9

• S = (7x9x7) x 4

Multiple Choice

• 164.9 cm²

• 277.0 cm²

• 138.5 cm²

• 191.3 cm²

​Volume

• Volume is the amount of space inside a 3-dimensional object and is measured in units³

• Word problems usually involve filling an object

• If a cone and a cylinder have the same radius & height, the volume of the cylinder will be 3 times the volume of the cone. Or the volume of the cone will be 1/3 the volume of the cylinder.

• When missing height, area of base, or radius, use nSolve

Multiple Choice

A bowling ball shaped like a sphere has a diameter of 21.6 centimeters. Which measurement is closest to the volume of the bowling ball in cubic centimeters?

• 1,954.3 cm³

• 5,276.7 cm³

• 488.6 cm³

• 42,213.4 cm³

Multiple Choice

Which measurement is closest to the volume of the party hat in cubic inches?

• 84.82 in³

• 339.29 in³

• 254.47 in³

• 1,017.88 in³

Multiple Choice

A cylinder and its dimensions are shown in the diagram. Which equation can be used to find V, the volume of the cylinder in cubic inches?

• ​ $$v=\pi\left(7.5h\right)^2$$

• $$v=\pi\left(7.5\right)^2h$$

• $$v=\pi\left(15\right)^2h$$

• $$v=\pi\left(15h\right)^2$$