A right triangle of hypotenuse 13 cm and one of its sides 12 cm is made to revolve
taking side 12 cm as its axis. Find the
volume and curved surface area of the solid
so formed.

9514 1404 393

Step-by-step explanation:

The other leg of the right triangle is found from the Pythagorean theorem:

  r² + 12² = 13²

  r = √(169 -144) = √25 = 5

The solid of revolution is a cone with a radius of 5, a height of 12, and a slant height of 13.

The volume is given by ...

  V = (1/3)πr²h

  V = (1/3)π(5 cm)²(12 cm) = 100π cm³ . . . volume

__

The lateral surface area is given by ...

  LA = πrh . . . where h is the slant height

  LA = π(5 cm)(13 cm) = 65π cm² . . . curved surface area

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2