Question

A cylindrical tin of height h cm and radius r cm, has surface area, including

its top and bottom, Acm2.

(i) Write down an expression for A in terms of r, h and π.

(ii) A tin of height 6cm has surface area 54πcm2

. What is the radius of the tin?

(iii) Another tin has the same diameter as height. Its surface area is 150πcm2.

What is its radius​

Answer 1

$\mathcal{\huge{\underline{\underline{\red{Question:-}}}}}$

A cylindrical tin of height h cm and radius r cm, has surface area, including its top and bottom, A cm².

$\mathcal{\huge{\underline{\underline{\red{Solution:-}}}}}$

• height of cylinder = h cm
• radius of cylinder = r cm

$\tt\Huge\pink{therefore:-}$

$\tt\Huge\blue{area =}$$\huge{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{πr²h cm² }}}}$

${\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow}$

• height of tin = 6 cm
• surface area = 54π cm²

$\mathcal{\huge{\underline{\underline{\red{To\:find:-}}}}}$

$\large\tt{radius\:of\:the\:tin}$

basic information ➡️

area of tin = $\huge{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{πr²h}}}}$

∴ 54π = πr²6

→ r² = 9

→ r = √9

→ r = 3

∴ $\mathcal{\huge{\fbox{\fbox{\red{radius=3}}}}}$

${\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow}$

$\mathcal{\huge{\underline{\underline{\red{Given\:that:-}}}}}$

$\rm\underline\green{height\:of\:tin\:is\: radius}$

∴

$\mathcal{\huge{\fbox{\fbox{\red{r = h }}}}}$

• surface area = 150π cm²

$\mathcal{\huge{\underline{\underline{\red{To\:find}}}}}$

→ radius of tin .

$\mathcal{\huge{\underline{\underline{\red{Solution:-}}}}}$

surface area = πr²h

$\blue{\tt{150π = πr²2r}}$

$\blue{\tt{150 = 2r³}}$

$\blue{\tt{r³ = 75}}$

$\blue{\tt{r = \sqrt[3]{ 75}}}$