Question

if a+b+c=π then sin^2a-sin^2b-sin^2c=-2cosa.sinb.sinc

Answer 1

Answer:

Answer:

r = 3 cm

Given:

Total Surface Area = 66π cm²

Height of the cylinder = 8 cm

To Find:

Radius of the cylinder = ?

Steps:

Formula to calculate the Total Surface Area of a cylinder is given as:

\boxed{ \text{TSA of cylinder} = 2 \pi r ( r + h )}

TSA of cylinder=2πr(r+h)

Substituting the given information in the formula we get:

\begin{gathered}\implies 66 \pi = 2\pi r ( 8 + r )\\\\\\\text{Transposing 2} \: \pi\: \text{to the LHS we get,}\\\\\\\implies \dfrac{ 66 \pi}{2 \pi} = r ( 8 + r )\\\\\\\implies 33 = 8r + r^2\\\\\\\implies r^2 + 8r - 33 = 0\\\\\\\text{Solving this equation we get,}\end{gathered}

⟹66π=2πr(8+r)

Transposing 2πto the LHS we get,

⟹

2π

66π

=r(8+r)

⟹33=8r+r

2

⟹r

2

+8r−33=0

Solving this equation we get,

\begin{gathered}\implies r^2 + 11r - 3r - 33 = 0\\\\\\\implies r ( r +11 ) - 3 ( r + 11 ) = 0\\\\\\\implies ( r + 11 ) ( r -3 ) = 0\\\\\\\implies r = (-11) \:\: and \:\: 3\\\\\text{But since 'r' cannot be negative we eliminate}\:\:-11.\:\:\text{Hence we get,}\\\\\implies \boxed{\bf{r = 3\:cm}}\end{gathered}

⟹r

2

+11r−3r−33=0

⟹r(r+11)−3(r+11)=0

⟹(r+11)(r−3)=0

⟹r=(−11)and3

But since ’r’ cannot be negative we eliminate−11.Hence we get,

⟹

r=3cm

Hence the radius of the base of the cylinder is 3 cm.