Surface Area and Volume

Surface Area and Volume

SOL G.13

Symbols used in this unit

• S.A. is the surface area which means the area that covers/surrounds a figure.

• V is the volume which means how much can an objected be filled or hold or contain.

• r = radius

• B = base area (the base is usually the polygon or circle that a 3 dimensional figure "stands" on)

• l = length, w=width, h= height (perpendicular distance)

•  $\pi$  is the Greek letter "pi" and equals approximately 3.14 (use the key on Desmos Calculator.

• DESMOS Calculator is expected to be used when solving!

Common Formula

these formulas are given to you on the Formula Sheet for the VA SOL test.

Note: B = base Area and b = length of the base of an object

Multiple Choice

 $A=\frac{bh}{2}$  where b is the base (that the height touches) and h is the height 

What is the Area of a triangle? 

• 20 cm²

• 56 cm²

• 28 cm²

• 27 cm²

Multiple Choice

 $A=\ bh$  where b= base and height is the perpendicular distance from base to opposite side.

What is the area of this parallelogram?

• 75 square cm

• 35 square cm

• 15 square cm

• 105 square cm

Multiple Choice

 $A\ =\ \frac{h\left(b_1+b_2\right)}{2}$  where b are the parallel bases. 

Find the area of the trapezoid.

• 18 m²

• 165 m²

• 84 m²

• 22.5 m²

Multiple Choice

What is the area of this circle?  $A=\pi r^2$  where r is the radius and the radius is half the diameter and use  $\pi$  on demos calculator (3.14) 

• 163.2

• 15.3

• 124.2

• 113.1

Multiple Choice

Calculate the volume.  To find the volume find the area of the triangle base and multiply by the height of the figure.  $V=Bh,$  where B is area of triangle, h is length of rectangle. 

•  90 cm³

• 150 cm³

• 180 cm³

Multiple Choice

 $V=lwh$  in this figure  $l=12,\ w\ =5.1,\ h\ =7$  

 Find the Volume

• 428.4 cm³

• 412.8 cm³

• 404.2 cm³

• 400 cm³

Multiple Choice

 $SA\ =\ 2lw+2lh\ +2wh$  In this figure  $l=15,\ w=10,\ h=10$  
What is the surface area of this figure?

• 200 cm ²

• 800 cm ²

• 400 cm ²

• 100 cm ²

Multiple Choice

 $S.A.=hp\ +2B$  in this firgure h=8, p=perimeter of triangle and B= area of triangle base. 

Find the total surface area of the prism.

• 161 square feet

• 1,700 square feet

• 75 square feet

• 186 square feet

Solid Figures

Cylinder, Sphere, Cone, Pyramid

Multiple Select

 $S.A.\ =\ 2\pi r^2+2\pi rh$  in this picture  $r=4,\ h\ =11$  

What is the surface area of the cylinder?

• 176π cm²

• 376.8 cm³

• 376.8 cm²

• 120π cm²

Multiple Choice

 $S.A.=\frac{1}{2}lp+B$ in this picrture $l\$  = 4 (height of triangle face), p = 4(2)= pereimeter of square base, B=2(2) = area of the square base. 

Find the Surface Area

• 15m²

• 16m²

• 18m²

• 20m²

Multiple Choice

 $S.A.\ =\ \pi rl$  

If slant height,  $l$ , of the cone is 21 cm and the diameter (2r) of the base is 24 cm. The total surface area of a cone is:

• 1200.77 sq.cm

• 1177 sq.cm

• 1222.77 sq.cm

• 1244.57 sq.cm

Multiple Choice

 $S.A.=4\pi r^2$  The surface area of a sphere of radius 14 cm is:

• 1386 sq.cm

• 1400 sq.cm

• 2464 sq.cm

• 2000 sq.cm

Multiple Choice

 $S.A.=\frac{1}{2}\left(4\pi r^2\right)$  

Find the surface area of the hemisphere (half a sphere)

• 339.3 in²

• 226.1in²

• 113.0 in²

• 452.2 in²

This concludes a summary of Surface Area and Volume

Please ask questions to help you understand. Please use DESMOS calcultor to help the calculations. Refer to the lesson Plan for more practice.