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?
Answers
Answer:
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:-}}}}}
Solution:−
height of cylinder = h cm
radius of cylinder = r cm
\tt\Huge\pink{therefore:-}therefore:−
\tt\Huge\blue{area =}area= \huge{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{πr²h cm² }}}}
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:-}}}}}
Tofind:−
\large\tt{radius\:of\:the\:tin}radiusofthetin
basic information ➡️
area of tin = \huge{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{πr²h}}}}
πr²h
∴ 54π = πr²6
→ r² = 9
→ r = √9
→ r = 3
∴ \mathcal{\huge{\fbox{\fbox{\red{radius=3}}}}}
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:-}}}}}
Giventhat:−
\rm\underline\green{height\:of\:tin\:is\: radius}
heightoftinisradius
∴
\mathcal{\huge{\fbox{\fbox{\red{r = h }}}}}
r = h
surface area = 150π cm²
\mathcal{\huge{\underline{\underline{\red{To\:find}}}}}
Tofind
→ radius of tin .
\mathcal{\huge{\underline{\underline{\red{Solution:-}}}}}
Solution:−
surface area = πr²h
\blue{\tt{150π = πr²2r}}150π=πr²2r
\blue{\tt{150 = 2r³}}150=2r³
\blue{\tt{r³ = 75}}r³=75
\blue{\tt{r = \sqrt[3]{ 75}}}r=
3
75
Step-by-step explanation:
hope it helps....
Answer:
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