Question

A solid right circular cone has height 4 cm and radius of its base is 3 cm. This cone is cut vertically along the plane passing through a diameter of the base. 'A' denotes the total surface area of the right circular cone while 'B' denotes the sum of the total surface areas of the two parts of the cone. Find A: B.
a) pi:(2pi+1) b) 2pi:(pi+3) c) pi:(pi+1) d) none of these ​

Answer 1

Answer:

Sssooorrryyy I don't know

Answer 2

Given a right-circular cone of base radius 'r' $3$cm and height 'h' $4$cm.

Explanation:

1. we have been provided with a right circular cone with base radius r($3$cm)  

   and height h($4$cm). hence the slant height of the cone is, $l=\sqrt{r^2+h^2}$

2. putting the value of r and h we get, $l=5\ cm$  

3. now, let A be the total surface area of the right circular cone , then A is  

   given by,         $A=\pi r(l+r)$

                           $A=24\pi \ cm^2$       ---(i)

4.now what happens is that the right circular cone is cut vertically along the

  diameter. since its cut along the diameter it forms two equal halves.

5. as its equally divided, the total surface area from original cone also gets

   divided. But due the division a new triangular surface is also formed at

   the plane of division.

6.This triangular area adds to the surface area of each conical halves. let B

   be the sum of total surface areas of two parts of cone then we get:  

  $B=(TSA\ of\ cone)+(2\ x\ area\ of triangle\ along\ division\ plane)$  

7. now , the base of the triangular plane be 'b' and perpendicular height be

   'H', then

                       $b=diameter\ of\ base = 6\ cm$

                       $H=height\ of\ cone= 4\ cm$

  then area of triangle $=$ $\frac{b(H)}{2}=12\ cm^2$       ---(ii)

8. from (i) and (ii) we get,     $B=24(\pi +1)$     ---(iii)

9. from (i) and (iii) we get,  $A:B=\pi :(\pi +1)$        => option (c) is the answer