Mastering Math with Rachel

Mastering Math with Rachel

Surface area of cylinders and rectangular prisms

Notes:

• A polyhedron is a solid figure whose faces are all polygons.

• A rectangular prism is a polyhedron in which all six faces are rectangles.

• A rectangular prism has eight vertices and 12 edges.

• A cylinder is a solid figure formed by two congruent parallel faces called bases joined by a curved surface.

• A face is any flat surface of a solid figure.

• The surface area of a prism is the sum of the areas of all 6 faces and is measured in square units.

• The volume of a three-dimensional figure is a measure of capacity and is measured in cubic units.

Notes continued:

• Nets are two-dimensional representations of a three-dimensional figure that can be folded into a model of the three-dimensional figure.

• A rectangular prism can be represented on a flat surface as a net that contains six rectangles — two that have measures of the length and width of the base, two others that have measures of the length and height, and two others that have measures of the width and height.

• The surface area of a rectangular prism is the sum of the areas of all six faces (𝑆𝐴 = 2𝑙𝑤 + 2𝑙ℎ + 2𝑤ℎ).  A cylinder can be represented on a flat surface as a net that contains two circles (the bases of the cylinder) and one rectangular region (the curved surface of the cylinder) whose length is the circumference of the circular base and whose width is the height of the cylinder.

• The surface area of the cylinder is the sum of the area of the two circles and the rectangle representing the curved surface (𝑆𝐴 = 2𝜋𝑟 2 +2𝜋𝑟ℎ).

• The volume of a rectangular prism is computed by multiplying the area of the base, B, (length times width) by the height of the prism (V = lwh = Bh).

• The volume of a cylinder is computed by multiplying the area of the base, B, (r 2 ) by the height of the cylinder (V = r 2h = Bh).

• The calculation of determining surface area and volume may vary depending upon the approximation for pi. Common approximations for π include 3.14, 22 7 , or the pi button on the calculator

Multiple Choice

A cylindrical paint can has a diameter of 12 centimeters and a height of

16 centimeters. Which is closest to the volume of the paint can in

cubic centimeters?

• 603

• 1,206

• 1,809

• 7,235

Multiple Choice

A cylindrical-shaped water tank has a diameter of 4 feet and is 12 feet tall. Which is closest to the volume of this tank?

• 48 cubic feet

• 151 cubic feet

• 452 cubic feet

• 603 cubic feet

Multiple Choice

What is the total surface area of this prism?

Length- 3 in.

Width - 4 in.

Height- 14 in.

• 110 square inches

• 168 square inches

• 208 square inches

• 220 square inches

Multiple Choice

Find the surface area of the cylinder. (use π = 3.14)

(𝑆𝐴 = 2𝜋𝑟 2 +2𝜋𝑟ℎ)

• 13.04 in2

• 113.04 in2

• 1.04 in2

• 23.04 in2

Multiple Choice

Find the volume of a rectangular prism with a length of 5 ft, width 6 ft, and height of 10 ft.

• 30 ft cubed

• 300 ft cubed

• 30 ft squared

• 3000 ft