Exercise 12 Page 755

Consider the given 3-D figure.

We identify this solid as a cone. Let's first calculate the surface area and then the volume.

Surface Area

To calculate the surface area of a cone, we can use the known formula where r is the radius of the base and l is the slant height of the cone. S=π rl+π r^2 To find the slant height, we can use the Pythagorean Theorem. When doing this, the slant height l is the hypotenuse. The height and radius of the cone are the legs. We are given that r= 5 and h= 6. Let's use the given values to calculate l.

a^2+b^2=c^2

SubstituteII

a= 5, b= 6

5^2+ 6^2=l^2

▼

Solve for l

CalcPow

Calculate power

25+36=l^2

AddTerms

Add terms

61=l^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(61)=l

RearrangeEqn

Rearrange equation

l=sqrt(61)

Now that we know the slant height, we can substitute r and l into the surface area formula.

S=π rl+π r^2

SubstituteII

r= 5, l= sqrt(61)

S=π( 5)( sqrt(61))+π( 5)^2

▼

Evaluate right-hand side

CalcPow

Calculate power

S=π(5)(sqrt(61))+π (25)

CommutativePropMult

Commutative Property of Multiplication

S=5sqrt(61)π+25π

FactorOut

Factor out π

S=(5sqrt(61)+25)π

UseCalc

Use a calculator

S=201.222931...

RoundDec

Round to 1 decimal place(s)

S≈ 201.2

The surface area of the cone is approximately 201.2m^2.

Volume

To calculate the volume of a cone, we can use the following formula. V= 13π r^2 h Here r is the radius and h is the height of the cone. Let's substitute these given values into the above formula and calculate the volume.

V=1/3π r^2 h

SubstituteII

r= 5, h= 6

V=1/3π ( 5)^2 ( 6)

▼

Evaluate right-hand side

CalcPow

Calculate power

V=1/3π(25)(6)

MoveRightFacToNumOne

1/b* a = a/b

V=150π/3