Question

find the total surface area and volume of a cone whose height is 28cm
and diameter is 42 cm​

Answer 1

Answer:

• Total surface area of cone is 3696 cm².
• Volume of cone is 12936 cm³.

Step-by-step explanation:

Given :-

• Height of cone is 28 cm.
• Diameter of cone is 42 cm.

To find :-

• Total surface area.
• Volume of cone.

Solution :-

Radius = Diameter/2

= 42/2

= 21

Radius (r) is 21 cm.

l = √r² + h²

Where,

• l is slant height, r is radius and h is height of cone.

$\sf \rightarrow l = \sqrt{(21)^{2} + {(28)}^{2} }$

$\sf \rightarrow l = \sqrt{441 + 784}$

$\sf \rightarrow l = \sqrt{1225}$

$\sf \rightarrow \bold{l = 35}$

Slant height (l) is 35 cm.

Now,

Total surface area of cone = πr² + πrl

$\longrightarrow$ T.S.A = 22/7 × (21)² + 22/7 × 21 × 35

$\longrightarrow$ T.S.A = 22/7 × 441 + 22/7 × 735

$\longrightarrow$ T.S.A = 9702/7 + 16170/7

$\longrightarrow$ T.S.A = 1386 + 2310

$\longrightarrow$ T.S.A = 3696

Thus,

Total surface area of cone is 3696 cm².

We know,

Volume of cone = 1/3 πr²h

$\longrightarrow$ Volume = 1/3 × 22/7 × (21)² × 28

$\longrightarrow$ Volume = 1/3 × 22/7 × 441 × 28

$\longrightarrow$ Volume = 1/3 × 22/7 × 12348

$\longrightarrow$ Volume = 271656/21

$\longrightarrow$ Volume = 12936

Therefore,

Volume of cone is 12936 cm³.

Answer 2

$\\ \: \color{blue}\underline{ \large\rm{Question :- }}$

→ find the total surface area and volume of a cone whose height is 28cm and diameter is 42 ccm.

$\\ \: \color{blue}\underline{ \large\rm{Answer :- }}$

$\star$ Total surface area of cone = 3696cm²

$\star$ Volume of cone = 12936 cm³

$\\ \: \color{blue}\underline{ \large\rm{Given :- }}$

$\star$ Height = h = 28 cm

$\star$ Diameter = d = 42

$\\ \: \color{blue}\underline{ \large\rm{Solution :- }}$

Here, d = 42 cm

First we have to find the radius , so

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: diameter \: = radius \times 2 \\ \\ \color{grey} \sf \: \therefore \: radius \: = \frac{42}{2} = 21cm^{2}$

Now ,

we have to find slant height

$\\ \purple{ \underline{\boxed{ \: \: \: \: \: \sf \: (l) \: slant \: height = \sqrt{(height) ² + (radius) ²} \: \: \: \: }}}$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \: \sqrt{ {(28)}^{2} + {(21)}^{2} }$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \: \sqrt{784 + 441 }$

$\\ \sf \: \: \: \: \: \: \: : \implies \: \: \sqrt{1225 }$

$\\ \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink{ \boxed{{ \frak{ l = 35 cm }}}}$

Now,

we have to find the total surface area of cone,

$\\ \color{purple}\underline{ \boxed{ \: \: \: \: \: \: \: \sf \: total \: surface \: area \: of \: cone \: = \pi \: radius(length + radius) \: \: \: \: \: \: \: \: }}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \: \sf \: \frac{22}{7} \times 21(35 + 21)$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \: \sf \: \frac{22}{7} \times 21 \times 56$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \: \sf \: 66 \times 56$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink{ \boxed{\frak{ \: \: \: \: \: \: \: \: \: \: \: total\: \: surface \: \:area \: \: cone = 3696 \: cm²}}}$

Now,

we have to find the volume of cone ,

$\\ \color{purple}\underline{ \boxed{ \: \: \: \: \: \: \: \sf \: volume\: of \: cone = \frac{1}{3} \times \pi \times \: radius^{2} \times height\: \: \: \: \: \: \: \: }}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \: \sf \: \frac{1}{3} \times \frac{22}{7} \times( 21) ^{2} \times 28$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \: \sf \: 22\times 21 \times 28$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \implies \: \: \sf \: 462\times 28$

$\\ \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink{ \boxed {\frak{ volume \: of \: cone = \: \: 12936 \: cm \: ^{3}}} }$

$\\ \: \color{blue}\underline{ \large\rm{Formulae :- }}$

$\: \: \: \: \bigstar \: \: \: \sf \: \: slant \: height = \sqrt{(height) ² + (radius) ²} \: \: \: \:$

$\: \: \: \: \bigstar\: \: \: \: \: \: \sf \: volume\: of \: cone = \frac{1}{3} \times \pi \times \: radius^{2} \times height\: \: \: \: \: \: \: \:$

$\: \: \: \: \bigstar \: \: \: \sf \: total \: surface \: area \: of \: cone \: = \pi \: radius(length + radius) \: \: \: \: \: \: \: \:$