1.
A metal washer is made from two concentric circles and its a ring shape.
Let r1= the radius of inner circle
r2= the radius of outer circle
Surface are
A=πr22−πr12 Given 2r1=21in,2r2=1in.
Then
r1=41in,r2=21in
A=π(21in)2−π(41in)2=163πin2The area of one of the washer is 163π in2.
2. From the description of the given word problem, the vertical end of a trough is a trapezoid.
Given a=4.4ft,b=3.2ft,h=3.5ft.
The area of a trapezoid is A=2a+bh.
Substitute
A=24.4ft+3.2ft(3.5ft)=13.3ft2The area of the end of the trough is 13.3ft2.
3. The curved surface area of the dome is
A=21(4πr2)=2πd2 Given d=36ft=432in. Then
2π(432in)2=93312π in2What must be paid for the golf leaf?
93312π in2(0.15$/in2)=$43972.25
4. Volume of one billiard ball
V1=34πr3=6πd3 Given d=21in=1.75ft. Then the volume of 1000 ivory billiard balls is
V=1000⋅6π(1.75ft)3=65359.375π ft3 The weight (mass) of 1000 ivory billiard balls is
M=ρV
M=114lb/ft3⋅(65359.375π ft3)
=319902.5 lb=145105.21 kg
The weight (mass) of 1000 ivory billiard balls is 319902.5 lb or 145105.21 kg.
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