Question

if r unit is the radius and 2l unit is rhe slant height of a right circular cone , then the total surface area is.
a) πr(l+r)
b) 3πrl sq.unit
c) 2πrl sq unit
d) πr (r/4 + l ) sq unit​

Answer 1

Answer:

Correct option is

B

πr(l+

4

r

)

We know, the total surface area of cone=πr(r+l).

Given, radius =

2

r

and slant height =2l.

Therefore, the new total surface area of cone =π×

2

r

(

2

r

+2l)

=π(

4

r

2

+rl)

=πr(l+

4

r

).

Therefore, option B is correct.

Answer 2

Note: there is mistake in the given question as it should be,

if $\frac{r}{2}$ unit is the radius and $2l$ unit is rhe slant height of a right circular cone , then the total surface area is.

a)   $\[\pi r\left( {l + r} \right)\]$ sq. units.   b) 3πrl sq.unit     c) 2πrl sq unit    d) $\[\pi r\left( {\frac{r}{4} + l} \right)\]$ sq unit​

Given: radius of the tright circular cone$=\frac{r}{2}$

Slant height of the right circular cone$=2l$

To find: the total surface area of the right circular cone.

Solution:

Find the total surface area (TSA) of the right circular cone.

Apply, $\[TSA = \pi r\left( {r + l} \right)\]$.

$\[ \Rightarrow TSA = \pi \times \frac{r}{2}\left( {\frac{r}{2} + 2l} \right)\]$

$\[ \Rightarrow TSA = \pi \times \frac{r}{2}\left( {\frac{{r + 4l}}{2}} \right)\]$

$\[ \Rightarrow TSA = \pi \times r\left( {\frac{{r + 4l}}{4}} \right)\]$

$\[ \Rightarrow TSA = \pi \times r\left( {\frac{r}{4} + l} \right)\]$ sq. units.

Therefore, the  total surface area (TSA) of the right circular cone is $\[\pi \times r\left( {\frac{r}{4} + l} \right)\]$sq. units.

Hence,the correct answer is option D. i.e., $\[\pi \times r\left( {\frac{r}{4} + l} \right)\]$sq. units.