Question

$\large \dag \; {\underline{\underline{\pmb{\purple{\sf{ \; Question \; :- }}}}}}$

$\longmapsto$ The Volume of a right circular cone is 9856 cm³ .If the Diameter of the Base is 28 cm .Find :-


i) Height of the Cone
ii) Slant Height of the Cone
iii) Curved Surface Area

$\\ \qquad{\rule{175pt}{2pt}}$

$\large \dag \; {\underline{\underline{\pmb{\orange{\sf{ \; Note \; :- }}}}}}$

$\dashrightarrow$ Kindly Don't Spam .
$\dashrightarrow$ Proper Explaination Required .
$\dashrightarrow$ Thanks in Advance :)

$\\ \qquad{\rule{175pt}{2pt}}$​

Answer 1

Answer:

is on top.

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Answer 2

Solution:

• Here, we're given with the volume of right circular cone i.e., 9856 cm³ and the diameter of base is 28 cm. We've been asked to calculate it's height, slant height and curved surface area.

The diameter of the base of cone is given as 28 cm. So, we can calculate it's radius as diameter is twice the radius. We can write it as:

$\twoheadrightarrow\quad\sf{d=2\times r}$

Substituting the value of diameter (28 cm) in the formula, we get:

$\twoheadrightarrow\quad\sf{28=2\times r}$

Now, transposing 2 from RHS to LHS. It's arithmetic operator will get changed.

$\twoheadrightarrow\quad\sf{\dfrac{28}{2}=r}$

Now, performing division in order to calculate radius.

$\twoheadrightarrow\quad\sf{r=14\; cm}$

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( I ) Let's calculate the height of the cone by substituting the values (provided in question) in VOLUME OF CONE formula:

$\longrightarrow\quad\rm{Volume\: of\: cone=\dfrac{1}{3}\times \pi\times {r}^{2}\times h}$

Now, equating the values:

$\longrightarrow\quad\rm{9856=\dfrac{1}{3}\times \dfrac{22}{7}\times {14}^{2}\times h}$

Equating the value of 14².

$\longrightarrow\quad\rm{9856=\dfrac{1}{3}\times \dfrac{22}{\cancel{7}}\times \cancel{196}\times h}$

Performing division.

$\longrightarrow\quad\rm{9856=\dfrac{1}{3}\times 22\times 28\times h}$

Now, performing multiplication.

$\longrightarrow\quad\rm{9856=\dfrac{616}{3}\times h}$

Transposing 616/3 from RHS to LHS. It's arithmetic operator will get changed.

$\longrightarrow\quad\rm{\cancel{9856}\times \cancel{\dfrac{3}{616}}=h}$

Performing multiplication and division, we get:

$\longrightarrow\quad\boxed{\rm{h=48\; cm}}$

❝Therefore, the height of cone is 48 cm.❞

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( II ) Let's calculate slant height of cone by l²=r²+h².

$\longrightarrow\quad\rm{{l}^{2}={r}^{2}+{h}^{2}}$

Substituting the given values:

$\longrightarrow\quad\rm{{l}^{2}={(14)}^{2}+{(48)}^{2}}$

Now,

$\longrightarrow\quad\rm{l=\sqrt{196+2304}}$

Now, performing addition.

$\longrightarrow\quad\rm{l=\sqrt{2500}}$

Now,

$\longrightarrow\quad\boxed{\rm{l=50\; cm}}$

❝Therefore, the slant height of cone is 50 cm.❞

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( III ) Let's calculate the curved surface area of cone by its formula:

$\longrightarrow\quad\rm{C.S.A\; of\; cone=\pi\times r\times l}$

Substituting the values:

$\longrightarrow\quad\rm{C.S.A\; of\; cone=\dfrac{22}{7}\times 14\times 50}$

Dividing 14 by 7.

$\longrightarrow\quad\rm{C.S.A\; of\; cone=22\times 2\times 50}$

Performing multiplication.

$\longrightarrow\quad\boxed{\rm{C.S.A\; of\; cone=2200\; {cm}^{2}}}$

❝Therefore, the curved surface area of cone is 2200 cm².❞