Question

A mailbox is 15 inches long and 8 inches wide. The height of the mailbox before the curve is 6 inches. What is the volume of the mailbox? Use 3.14 for pi.

Answer 1

we see that we can cut it up
1 rectangular prism (bottom part that is like a box0
1 half dome=1/2 cylinder


V of rectangular prism=LWH
v of cylinder=hpir^2

retangualr prism volume
L=15
W=8
H=6
V=15*6*8=720 in^2

1/2 cylinder
8=diameter
d/2=r
8/2=4=r
h=15
r=4
V=15pi4^2
v=15pi16
v=240pi
pi=3.14
v=753.6
half cylinder so multiply by 1/2
752.6 tiems 1/2=376.8 in^3

add
prism+1/2sphere=volume=720+376.8=1096.8 in^3



1096.8 in^3

Answer 2

First, we'll find the area of the base. (To find the volume of any prism, find the area of the base, then multiply by the length/height.) It consists of a rectangle and a semicircle put together. To find the area of the semicircle, we'll just use the formula for the area of a circle, then divide by two. Area of a circle = radius² × 3.14. If the diameter of this circle is 8, then halve that to find the radius, which is 4. 4² = 16. 16 × 3.14 = 50.24. Now, 50.24/2 = 25.12. 25.12 is the area of the semicircle. Then, find the area of the rectangle. Formula for that is base × height. 6 × 8 = 48. Now add the two areas. 25.12 + 48 = 73.12.
Simply multiply that area by the length to find the volume. 73.12 × 15 = 1096.8.
The volume of the mailbox is 1,096.8 in³. (Don't forget to label!)
Hope that helped!