Question

the sum of the radius of base and height of a solid right circular cylinder is 37cm.If the total surface area of the solid cylinder is 1628.Find its radius and height​

Answer 1

$\bold\green{:SOLUTION:}$

☆GIVEN☆

• The sum of radius and height of CYCLINDER=37cm
• The total surface area of CYCLINDER=1628cm²

☆LET

• The radius of CYCLINDER be r
• The height of CYCLINDER be h

☆FIND

• The radius and height of CYCLINDER

☆According to the above information☆

• by using formula of TSA
• here,(r+h)=37.....(1)

☆T S A OF CYCLINDER=1628☆

$↠T.S.A = 1628 \\ \\ ↠2\pi \: r(r + h) = 1628 \\ \\ ↠2 \times \frac{22}{7} \times r \times 37 = 1628 \\ \\ ↠2 \times 22 \times r \times 37 = 1628 \times 7 \\ \\ ↠r = \frac{1628 \times 7}{2 \times 22 \times 37} \\ \\ ↠r = 7cm$

☆PUTTING THE VALVE OF r IN (r+h)=37

$⟹r + h = 37 \\ \\ ⟹7 + h = 37 \\ \\ ⟹h = 37 - 7 \\ \\ ⟹h = 30$

✺HENCE✺

• The radius of CYCLINDER=7cm
• The height of CYCLINDER=30cm

$\boxed{\green{\sf{\ \ {\tex{ANSWER=> r=7 ,h=30}}}}}$

Answer 2

$\huge\underline\purple{Solution:}$

$\sf{Given=\begin{cases}The\:sum\:of\:r+h=37\\T.S.A=1628\end{cases}}$

$\sf{\implies 2\pi\:r(h+r)=1628}$

$\sf{\implies 2*\dfrac{22}{7}*r*37=1628}$

$\sf{\implies \dfrac{2*22*r*37}{7}=1628}$

$\sf{\implies r=\dfrac{1628*7}{2*22*37}}$

$\sf\green{\implies R=7cm}$

$\sf{\implies Now,\: putting\:the\: value}$

$\sf{\implies r+h=37}$

$\sf{\implies 7+h=37}$

$\sf{\implies h=37-7}$

$\sf{\implies h=30}$

Therefore,

$\sf\red{\implies Radius\:of\: cylinder=7cm}$

$\sf\green{\implies Height\:of\: cylinder=30cm}$