8.6.A 8.6.B 8.7.A 8.7.B

Texas Essential Knowledge and Skills (TEKS) Surface Area & Volume
Grade:	8th Grade
Standard:	8.6.A
Description:	describe the volume formula V = Bh of a cylinder in terms of its base area and its height;
Standard:	8.6.B
Description:	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
Standard:	8.7.A
Description:	solve problems involving the volume of cylinders, cones, and spheres;
Standard:	8.7.B
Description:	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;

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}

Texas Essential Knowledge and Skills (TEKS)