MA.7.1.1 MA.7.1.2 MA.7.2.1 MA.7.2.2 MA.7.2.3

Surface Area & Volume 7th Grade

Florida - Benchmarks for Excellent Student Thinking: MA.7.1.1
Apply formulas to find the areas of trapezoids, parallelograms and rhombi
Florida - Benchmarks for Excellent Student Thinking: MA.7.1.2
Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.
Florida - Benchmarks for Excellent Student Thinking: MA.7.2.1
Given a mathematical or real-world context, find the surface area of a right circular cylinder using the figure’s net.
Florida - Benchmarks for Excellent Student Thinking: MA.7.2.2
Solve real-world problems involving surface area of right circular cylinders.
Florida - Benchmarks for Excellent Student Thinking: MA.7.2.3
Solve mathematical and real-world problems involving volume of right circular cylinders.

Volume Cylinder = n r^{2} h

where r is the radius and h is the height

\begin{array}{rcl} Volume & = & n r^{2} h \\ 1130.04 {cm}^{3} & = & n r^{2} h \\ 1130.04 {cm}^{3} & = & (3.14) r^{2} 10 \\ 1130.04 {cm}^{3} \div 3.14 & = & (3.14) r^{2} 10 \div 3.14 \\ 360 {cm}^{3} & = & r^{2} \\ 360 {cm}^{3} \div 10 & = & r^{2} 10 \div 10 \\ 36 {cm}^{3} & = & r^{2} \\ 5 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

Florida - Benchmarks for Excellent Student Thinking: MA.7.1.1

Apply formulas to find the areas of trapezoids, parallelograms and rhombi

Florida - Benchmarks for Excellent Student Thinking: MA.7.1.2

Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.

Florida - Benchmarks for Excellent Student Thinking: MA.7.2.1

Given a mathematical or real-world context, find the surface area of a right circular cylinder using the figure’s net.

Florida - Benchmarks for Excellent Student Thinking: MA.7.2.2

Solve real-world problems involving surface area of right circular cylinders.

Florida - Benchmarks for Excellent Student Thinking: MA.7.2.3

Solve mathematical and real-world problems involving volume of right circular cylinders.

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