math 6b sample work unit 8

1) Calculate the area of a rectangle with a length of 8 cm and a width of 5 cm.

Area = length x width
Area = 8 cm x 5 cm
Area = 40 cm²

2) Find the volume of a cube with a side length of 3 cm.

Volume = side length³
Volume = 3 cm x 3 cm x 3 cm
Volume = 27 cm³

3) Determine the circumference of a circle with a radius of 4 cm.

Circumference = 2πr
Circumference = 2 x π x 4 cm
Circumference = 8π cm

4) Solve for the missing side length of a right triangle with a base of 6 cm and a height of 8 cm.

Using the Pythagorean theorem,
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10 cm

The missing side length is 10 cm.

5) Calculate the surface area of a cylinder with a radius of 3 cm and a height of 10 cm.

Surface Area = 2πr² + 2πrh
Surface Area = 2 x π x (3 cm)² + 2 x π x 3 cm x 10 cm
Surface Area = 2π(9) + 60π
Surface Area = 18π + 60π
Surface Area = 78π cm²