Question

What is the total surface area of a cone having radius 35 cm and height 21 cm.
a) 6100 sq.cm. b) 2601 sq.cm. c) 6160 sq.cm d) 3240 sq.cm.​

Answer 1

${ \underline{ \red{ \tt{ \huge{ \underline{QUESTION }}}}}}$



▪ What is th e total surface area of the cone having radius 35 cm and height 21 cm.


a) 6100 sq. cm

b) 2601 sq. cm

c) 6160 sq. cm

d) 3240 sq. cm




${ \underline{ \red{ \tt{ \huge{ \underline{SOLUTION }}}}}}$



${ \star{ \purple{ \bold{ \: \: \: GIVEN }}}}$



${ \pink{ \underline{ \underline{ \sf{Dimension \: of \: cone}}}}}$



${ \blue{ \sf{ radius= 35 \: cm}}} \\ \\ { \blue{ \sf{height = 21 \: cm}}}$


${ \bold{ \underline{ \green{Total \: Surface \: Area}}}} \\ \\ { \boxed{ \boxed{ \tt{ \green{TSA = \pi \: r l + \pi \: {r}^{2} }}}}} \\ \\ { \sf{where}} \\ \\ { \sf{ \green{r = radius \: of \: the \: cone}}} \\ \\ { \sf{ \green{l = slant \: height \: of \: the \: cone}}}$




• Putting the given values in the formula....



${ \tt{ \pink{TSA = \pi \times 35cm \times 21cm \: + \: \pi \: {(35 cm)}^{2} }}} \\ \\ { \implies{\tt{ \pink{TSA = 35\pi \: (21 + 35) \: {cm}^{2} }}}} \\ \\ { \implies{ \tt{ \pink{TSA = \frac{22}{7} \times 35 \times 56 \: {cm}^{2} }}}} \\ \\ { \tt{ \implies{\pink{TSA = 22 \times 5 \times 56 \: {cm}^{2} }}}}$




${ \implies{ \boxed{ \boxed{ \red{ \sf{ \: Total \: Surface \: Area = 6160 \: {cm}^{2} \: }}}}}}$



thus,

☆ option (c) is correct



${ \bigstar{ \underline{ \purple{ \bold{ \: \: \: \: Other \: formulas \: for \: CONE}}}}}$



${ \sf{(1)}{ \underline{\: Volume}}} \\ \\ { \boxed{ \green{ \sf{V = \frac{1}{3} \pi \: {r}^{2} h}}}}$



${ \sf{(2){ \underline{ \: Lateral \: Area}}}} \\ \\ { \sf{ \boxed{ \green{Al = \pi \: rl}}}}$




${ \sf{(3){ \underline{ \: Base \: Area}}}} \\ \\ { \boxed{ \sf{ \green{Ab = \pi \: {r}^{2} }}}}$




${ \sf{(4){ \underline{ \: Height}}}} \\ \\ { \boxed{ \green{ \sf{h = 3 \times \frac{V }{\pi \: {r}^{2} } }}}}$




${ \sf{(5){ \underline{ \: Radius}}}} \\ \\ { \boxed{ \green{ \sf{r = \sqrt{3 \times \frac{V}{\pi \: h}}}}} }$



${ \sf{(6){ \underline{ \: Slant \: height}}}} \\ \\ { \boxed{ \green{ \sf{l = \sqrt{ {r}^{2} + {h}^{2} } }}}}$

Answer 2

${ \underline{ \huge{ \underline{SOLUTION }}}}$

${ \star{ \bold{ \: \: \: GIVEN }}}$

${ \underline{ \underline{ \sf{Dimension \: of \: cone}}}}$

${ \sf{ radius= 35 \: cm}}} \\ \\ { \blue{ \sf{height = 21 \: cm}}$

${ \bold{ \underline{ Total \: Surface \: Area}}} \\ { { \boxed{ \tt{ \green{TSA = \pi \: r l + \pi \: {r}^{2} }}}} \\ \\ { \sf{where}} \\ \\ { \sf{ \green{r = radius \: of \: the \: cone}}} \\ \\ { \sf{ \green{l = slant \: height \: of \: the \: cone}}}$

• Putting the given values in the formula....

${ \tt{ \pink{TSA = \pi \times 35cm \times 21cm \: + \: \pi \: {(35 cm)}^{2} }}} \\ \\ { \implies{\tt{ \pink{TSA = 35\pi \: (21 + 35) \: {cm}^{2} }}}} \\ \\ { \implies{ \tt{ \pink{TSA = \frac{22}{7} \times 35 \times 56 \: {cm}^{2} }}}} \\ \\ { \tt{ \implies{\pink{TSA = 22 \times 5 \times 56 \: {cm}^{2} }}}}$

${ \implies{ \boxed{ \boxed{ \red{ \sf{ \: Total \: Surface \: Area = 6160 \: {cm}^{2} \: }}}}}}$

thus,

☆ option (c) is correct

${ \bigstar{ \underline{ \purple{ \bold{ \: \: \: \: Other \: formulas \: for \: CONE}}}}}$

${ \sf{(1)}{ \underline{\: Volume}}} \\ \\ { \boxed{ \green{ \sf{V = \frac{1}{3} \pi \: {r}^{2} h}}}}$

${ \sf{(2){ \underline{ \: Lateral \: Area}}}} \\ \\ { \sf{ \boxed{ \green{Al = \pi \: rl}}}}$

${ \sf{(3){ \underline{ \: Base \: Area}}}} \\ \\ { \boxed{ \sf{ \green{Ab = \pi \: {r}^{2} }}}}$

${ \sf{(4){ \underline{ \: Height}}}} \\ \\ { \boxed{ \green{ \sf{h = 3 \times \frac{V }{\pi \: {r}^{2} } }}}}$

${ \sf{(5){ \underline{ \: Radius}}}} \\ \\ { \boxed{ \green{ \sf{r = \sqrt{3 \times \frac{V}{\pi \: h}}}}} }$

${ \sf{(6){ \underline{ \: Slant \: height}}}} \\ \\ { \boxed{ \green{ \sf{l = \sqrt{ {r}^{2} + {h}^{2} } }}}}$