8.6.a 8.6.b 8.7.a 8.7.b 7.GSR.6 7.GSR.8

Surface Area & Volume 8th Grade

Texas Essential Knowledge and Skills (TEKS): 8.6.a
describe the volume formula V = Bh of a cylinder in terms of its base area and its height;
Texas Essential Knowledge and Skills (TEKS): 8.6.b
model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; and
Texas Essential Knowledge and Skills (TEKS): 8.7.a
solve problems involving the volume of cylinders, cones, and spheres;
Texas Essential Knowledge and Skills (TEKS): 8.7.b
use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders;
Georgia Standards of Excellence (GSE): 7.GSR.6
Solve realistic problems involving surface area of right prisms and cylinders.
Georgia Standards of Excellence (GSE): 7.GSR.8
Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.

Volume Cone = \frac{1}{3} π r^{2} h

Volume Sphere = \frac{4}{3} π r^{3}

Volume Cylinder = π r^{2} h

where r is the radius and h is the height

\begin{array}{rcl} Volume & = & \frac{4}{3} π r^{3} \\ 113.04 {cm}^{3} & = & \frac{4}{3} π r^{3} \\ 113.04 {cm}^{3} & = & \frac{4}{3} (3.14) r^{3} \\ 113.04 {cm}^{3} \div 3.14 & = & \frac{4}{3} (3.14) r^{3} \div 3.14 \\ 36 {cm}^{3} & = & \frac{4}{3} r^{3} \\ 36 {cm}^{3} \times \frac{3}{4} & = & \frac{4}{3} r^{3} \times \frac{3}{4} \\ 27 {cm}^{3} & = & r^{3} \\ 3 cm & = & r \end{array}

The surface area of a three-dimensional figure is the total area of its surface.

The lateral area of a three-dimensional figure is
the surface area minus the area of the bases.

LATERAL AREA

Prism = Perimeter base × height

Cylinder = Circumference base × height

SURFACE AREA

Prism or Cylinder = Lateral Area + 2B

where B is the area of the base

To find the lateral area, first, find the circumference of the base of the cylinder.

Circumference	=	2 $π$ r
	=	2(3.14)(3 feet)
	=	18.84 feet

To find the surface area, first, find the area of the base of the cylinder.

Area	=	$π$ r^²
	=	3.14(3 feet)^²
	=	28.26 square feet

Surface Area & Volume

Texas Essential Knowledge and Skills (TEKS): 8.6.a

describe the volume formula V = Bh of a cylinder in terms of its base area and its height;

Texas Essential Knowledge and Skills (TEKS): 8.6.b

model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; and

Texas Essential Knowledge and Skills (TEKS): 8.7.a

solve problems involving the volume of cylinders, cones, and spheres;

Texas Essential Knowledge and Skills (TEKS): 8.7.b

use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders;

Georgia Standards of Excellence (GSE): 7.GSR.6

Solve realistic problems involving surface area of right prisms and cylinders.

Georgia Standards of Excellence (GSE): 7.GSR.8

Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.

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