Question

1. What is the length of sides x (adjacent side) and y (opposite side) in the triangle, if, (hyp=30 cm, and theta= 25^o)

2. What is the surface area of the sphere where r=80 cm? What is its volume?

3. If a gallon is 231 in³ and 1 in = 2.54 cm, how many cm³ are in a gallon?

Answer 1

1 )

given

hypotenus = 30 cm = hyp = 0.3 m

= 25^o

in a right angle triangle we have sin = opposite / hyp

hyp X sin = opposite = x

x = 0.3 X sin25

x = 0.1267 m

x = 12.67 cm

next cos = adjacent/ hyp

cos X hyp = adjacent = y

y = cos25 X 0.3

y = 0.2718

y = 27.18 cm

2 )

given r = 80 cm = 0.8 m

surface area = 4 r²

A = 4 X 3.14 X 0.8²

A = 8.0384 m²  

Volume = V = (4/3) r³   

V = (4/3) X 3.14 X 0.8³   

V = 2.1435 m³  

3 )

gallon is 231 in³

now each inch = 2.54 cm

1 cm³ = 2.54 X 2.54 X 2.54 = 16.387064 cm³

231 in³ = 231 X 16.387064 cm³ = 3785.411 cm³