Surface Area and Volume of 3D Solids

Rectangular Prisms

100

What is the formula for finding volume of a rectangular prism?

V = l * w * h

200

What is the formula for finding surface area of a rectangular prism?

SA = 2wl + 2lh + 2hw

300

Find the volume of a rectangular prism with the following dimensions:

length= 4m; width= 8m; height= 3m

V= l*w*h

=4*8*3

=96m³

400

Find the surface area of a rectangular prism with the following dimensions:

length= 11cm; width= 0.9cm; height= 22cm

SA= 2wl*2lh*2hw

=(2*0.9*11)+(2*11*22)+(2*22*0.9)

=19.8+484+39.6

=543.4cm²

500

Find the missing value:

length= 12 in; width= 3 in; V= 198in³

height= ?

V= l*w*h

198= 12*3*h

198= 36h

5.5in = h

Pyramids

100

What is the formula for finding volume of a pyramid?

V = 1/3 * base area * height

200

What is the formula for finding surface area of a pyramid?

SA = base area + (1/2 * perimeter * slant height)

300

Find the volume of a square pyramid with the following dimensions:

base side length= 6ft; height=7ft

V= 1/2*base area*height

=1/2*(6*6)*7

=126ft³

400

Find the surface area of a square pyramid with the following dimensions:

base side length= 6ft; slant height=7ft

SA= base area + 1/2 * perimeter * slant height

base area = 6*6 = 36ft²

perimeter= 6+6+6+6 = 24ft

SA= 36 + 1/2*24*7

= 120ft³

500

Find the missing value:

SA= 85m²; perimeter= 20m; slant height= 6m

base side length= ?

SA= base area + 1/2*perimeter*slant height

85= base area + 1/2*20*6

85= base area + 60

25= base area

base side length (square root of base area)= 5m

Triangular Prisms

100

What is the formula for finding volume of a triangular prism?

V= 1/2 * b * h * l

200

What is the formula for finding surface area of a triangular prism?

SA = (bh) + (s1+s2+s3)*l

300

Find the volume of a triangular prism with the following dimensions:

base= 4mm; height= 10mm; length of prism= 2mm

V= 1/2*b*h*l

=1/2*4*10*2

=40mm³

400

Find the surface area of a triangular prism with the following dimensions:

base of triangle face= 12yd; height= 8yd

side 1= 10yd; side 2= 10yd, side 3= 12yd

length of prism= 14yd

SA = (bh) + (s1+s2+s3)*l

= (12*8)+(10+10+12)*14

=96+ 32*14

=544yd²

500

Find the surface area of a triangular prism with the following dimensions:

area of 1 triangle face (1/2*b*h)= 30m²

side1= 3m; side2= 3m, side3= 6m

length of prism= 5m

SA = (bh) + (s1+s2+s3)*l

= 60+(12*5)

=120m²

Cones & Cylinders

100

What is the formula for finding volume of a cylinder?

V = 3.14 * r² * h

200

What is the formula for finding volume of a cone?

V = 3.14 * r² * h * 1/3

300

If a cone and a cylinder have the same radius and height, what will be the relationship between their volumes?

Volume of a Cone = 1/3 Volume of a Cylinder

400

What is the volume of a cone with the following dimensions:

diameter= 4.4cm; height= 5.1cm

(round to the nearest tenth)

V = 3.14 * r² * h * 1/3

=3.14* 2.2²* 5.1* 1/3

=25.8 cm³

500

Find the missing value:

Volume of a cylinder= 549.5in³; diameter= 10in

height= ?

V = 3.14 * r² * h

549.5= 3.14*25*h

549.5= 78.5*h

h= 7in

Random Geometry

100

Which term is used to describe flipping an object across a line without changing its size or shape?

A. translation

B. reflection

C. rotation

B. reflection

200

Which point falls in quadrant 3 on the coordinate plane?

A. (-9, -1)

B. (0, -1)

C. (3, 2)

A. (-9, -1)

300

Give an example of symmetry found in nature.

Ex: Butterfly wings pattern

400

How many lines of symmetry does a regular pentagon have?

5

500

How many degrees would I have to rotate the letter M to make it look like the letter W?

180 degrees