Substitute the given values in the formula and simplify.
B
b
Try thinking about how modifying the value for the radius or the slant height will affect the expression for the surface area. You can try using different values for them.
A
a
131.9 cm^()2
B
b
No, the surface area would not double. See solution.
S.A.=Ï€ r(l +r)
We know that the radius of the cone is 3 cm while the slant height is 11 cm. We are also told to use the approximate value of 3.14 for π. Let's substitute these values into the formula and simplify following the order of operations.
We got that the surface area of the cone is approximately 131.9cm^2.
b
Now that we know the value for the surface area is S=131.9 cm^()2, we can see if doubling the radius or the slant height will double the value of the surface area as well. If the area is doubled, it will have the following value.
S = 131.9 cm^()2 ⇒ 2S= 263.8 cm^2If the previously stated theory is true, we should get an area value of 263.8 as result after doubling either the original radius or the original slant height. Let's try by doubling the radius first.
r = 3 cm ⇒ 2r = 6 cm
We will now substitute r= 6 cm while keeping the original slant height l= 11 cm in the surface area formula. Then, we will verify if the original surface area doubles.
Doubling the radius does not double surface area. Let's try by doubling the slant height now.
l = 11 cm ⇒ 2l = 22 cm
We will substitute l= 22 cm while keeping the original radius r= 3 cm in the surface area equation, and verify if the original surface area doubles.
We now have an equivalent expression for the surface area.
S= π rl + π r^2 ⇒ 2S=2π rl + 2π r^2
We wanted to see if doubling the radius r or the slant height h doubles the surface area as well. Let's analyze what happens when doubling the radius in the distributed expression for the surface area.
r & ⇒ 2r
π rl + π r^2 & ⇒ π ( 2r)l + π ( 2r)^2
Let's simplify the expression to see if it is equivalent to 2S=2Ï€ rl + 2Ï€ r^2.
As we can see, the expressions are not equivalent. No matter what value for r we choose, doubling it will not double the surface area. In a similar way, we will now try doubling the slant height.
l & ⇒ 2l
π rl + π r^2 & ⇒ π r( 2l )+ π r^2
Let's rewrite the previous expression to see if it is equivalent to 2S=2Ï€ rl + 2Ï€ r^2.
