Question

In exercise 14 and 15, the value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x. then find the surface area and volume of the cylinder. 14)With the height of x and base of 6ft 15) with the height x and base of 10 m

Answer 1

Answer and explanation:

Volume of a cylinder = π r² h

Surface area of a cylinder = 2π r h + 2π r².

Since volume of cylinder = surface area of cylinder

π r² h=2π r h + 2π r²

Solving 14)

Given height x and base 6ft, radius will be 3ft

π r² h=2π r h + 2π r²

22/7*3²*x= 2*22/7*3*x+2*22/7*3²

=22/7*9*x= 2*22/7*3*x+2*22/7*9

= 28.286x=18.857x+2*28.286

=28.286x=18.857x+56.572

=9.429x=56.572

x=5.999ft( x cannot be a negative value)

15) Given height x and base 10 m, radius will be 5m

π r² h=2π r h + 2π r²

22/7*5²*x= 2*22/7*5*x+2*22/7*5²

78.5714x= 31.429x+157.1428

47.1424x=157.1428

x=3.333m( because x cannot be negative)