Manny is building a blanket chest for his sister.
His design is a composite of a square prism and
half of a cylinder.
What is the volume of the hope chest?
HELP ME PLEASE!!!
L = length of the hope chest
W = width of the hope chest
H = height of the hope chest
The volume of the prism is:
Vprism = L ∙ W ∙ H
Since the prism is a square, the width is equal to the height of the hope chest.
W = H
Vprism = L ∙ W ∙ H = L ∙ W ∙ W = W² ∙ L
W / 2 is also the radius of the half-cylinder.
r = W / 2
The volume of the half-cylinder is 1 / 2 of the volume of the cylinder:
Vhalf cylinder = 1 / 2 r² ∙ π ∙ L = 1 / 2 ( W / 2 )² ∙ π ∙ L =
1 / 2 ∙ W² ∙ π ∙ L / 4 = W² ∙ L ∙ π / 8
V = Volume of the hope chest = Vprism + Vhalf cylinder
V = W² ∙ L + W² ∙ L ∙ π / 8
V = W² ∙ L ∙ ( 1 + π / 8 )