Question

The total surface area of a cylinder is 40 pie cm^2. If height is 5.4 then its base radius is

Option
A. 5cm B. 2.5cm C. 1.5cm D. 10cm

Answer 1

Solution:

Given:

• Total Surface area of cylinder = 40 π cm²
• Height of cylinder = 5.4 cm

To Find:

• Radius of cylinder.

Formula used:

• $\rm{Total\;surface\;area\;of\;cylinder=2\pi r(r+h)}$

Now, put the values in the formula we get,

$\rm{\implies Total\;surface\;area\;of\;cylinder=2\pi r(r+h)}$

$\rm{\implies 40\times 3.14=2\times 3.14\times r(r+5.4)}$

$\rm{\implies 125.6=6.28r^{2}+33.912r}$

$\rm{\implies 6.28r^{2}+33.912r-125.6=0}$

Now, we will solve it by quadratic formula,

$\rm{\implies x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}}$

$\rm{\implies x=\dfrac{-33.9\pm\sqrt{(33.9)^{2}-4\times 6.28\times (-125.6)}}{2\times 6.28}}$

$\rm{\implies x=\dfrac{-33.9\pm\sqrt{1149.21+3155.072}}{12.56}}$

$\rm{\implies x=\dfrac{-33.9\pm\sqrt{4304.282}}{12.56}}$

$\rm{\implies x=\dfrac{-33.9\pm 65.607}{12.56}}$

$\rule{200}{2}$

$\rm{\implies x=\dfrac{-33.9+65.607}{12.56}}$

$\rm{\implies x=\dfrac{31.70}{12.56}}$

$\rm{\implies x=2.5}$

$\rule{200}{2}$

$\rm{\implies x=\dfrac{-33.9-65.607}{12.56}}$

$\rm{\implies x=-\dfrac{99.50}{12.56}}$

$\rm{\implies x=-7.9}$

$\rule{200}{2}$

We know that radius cannot be negative. Hence radius = 2.5 cm.

Answer 2

$\bold{\underline{\underline{\huge{\mathfrak{AnsWer:}}}}}$

$\bold{\underline{\boxed{\red{\sf{Radius\:of\:the\:base\:=\:2.5cm}}}}}$

$\bold{\underline{\underline{\large{\mathfrak{StEp\:by\:stEp\:explanation:}}}}}$

$\bold{\underline{\underline{\red{\tt{GiVeN:}}}}}$

• Total surface area of a cylinder is $\tt{40\:\pi\:cm^2}$
• Height = 5.4 cm

$\bold{\underline{\underline{\red{\tt{To\:FiNd:}}}}}$

• Base radius.

$\bold{\underline{\underline{\red{\tt{SoLuTioN:}}}}}$

Formula :

$\bold{\large{\red{\boxed{\tt{TSA_{cylinder}\:=\:2\pi\:r(h+r)}}}}}$

The values of,

• TSA = 40π cm²
• π = 22/7
• h = 5.4 cm

Block in the values,

$\longrightarrow$ $\tt{40\:\pi\:=\:2\:\pi\:r\:(5.4\:+r)}$

$\longrightarrow$ $\tt{40\:\pi\:=\:5.4(2\pi\:r)\:+\:r\:(2\:\pi\:r)}$

$\longrightarrow$ $\tt{40\:\pi\:=\:10.8\:\pi\:r\:+\:2\:\pi\:\:r^2}$

$\longrightarrow$ $\tt{2\:\pi\:r^2\:+\:10.8\:\pi\:r\:=\:40\:\pi}$

$\longrightarrow$ $\tt{2\:\pi\:r^2\:+\:10.8\:\pi\:r\:-\:40\:\pi\:=0}$

Solve using factorization method,

$\longrightarrow$ $\tt{2\:\pi\:r^2\:+\:10.8\:\times\:3.14\:r\:-\:40\:\pi\:=0}$

$\longrightarrow$ $\tt{2\:\pi\:r^2\:33.92\:r\:-\:40\:\pi\:=0}$

$\longrightarrow$ $\tt{2\:\times\:3.14\:r^2+\:33.92\:r\:-\:40\:\times\:3.14\:=0}=$

$\longrightarrow$ $\tt{6.28r^2\:+\:33.92\:r\:-125.6\:=\:0}$

$\longrightarrow$ $\tt{r\:(6.28\:r\:+\:33.92)\:-\:125.6\:=0}$

$\longrightarrow$ $\tt{6.28r^2\:+\:33.92r\:-\:125.6=0}$

$\longrightarrow$ $\tt{2\:\pi\:(r\:+\:2.7)^2\:-\:171.46\:=0}$

$\longrightarrow$ $\tt{2(3.14r^2\:+16.96r\:-62.83\:=\:0}$

$\longrightarrow$ $\tt{6.28\:r^2\:+\:33.92r\:-\:125.6\:=0}$

$\longrightarrow$ $\tt{r\:=\:-7.92\:\:OR\:\:r\:=\:2.5}$

Radius cannot be negative.

•°• r = - 7.92 is not acceptable.

$\tt{\therefore{Radius\:of\:the\:base\:=\:2.5cm}}$

A tip : Kindly refer to the answer of @Missayu for better explanation xD xD