Given the following information:

- (i) X is a cone with volume 1232 m³
- (ii) Y is a cylinder with volume 1848 m³
- (iii) S is a square inscribed in a circle

Match the following:

| Column I | Column II |
|--------------------------------------------|-------------------------------|
| (i) X = Cone | (A) Radius = 14 m |
| Volume of cone = 1232 m³ | |
| (ii) Y = Cylinder | (B) Radius = 7 m |
| Volume of cylinder = 1848 m³ | |
| (iii) S = Square, which inscribe in circle | (C) Circumference of circle = 44 m |

If the height of X is greater than the height of Y, which of the following matches are correct?

Select the correct combination:

(a) (i) Only A, (ii) Either B or C, (iii) Only A

(b) (i) Either B or C, (ii) Only A, (iii) Only A, either B or C

(c) (i) Only B, (ii) Only A, (iii) Only A

(d) (i) Only C, (ii) Only B, (iii) Only B

(e) None of these

Question

Given the following information:

- (i) X is a cone with volume 1232 m³
- (ii) Y is a cylinder with volume 1848 m³
- (iii) S is a square inscribed in a circle

Match the following:

| Column I                                   | Column II                     |
|--------------------------------------------|-------------------------------|
| (i) X = Cone                               | (A) Radius = 14 m            |
| Volume of cone = 1232 m³                   |                               |
| (ii) Y = Cylinder                          | (B) Radius = 7 m             |
| Volume of cylinder = 1848 m³               |                               |
| (iii) S = Square, which inscribe in circle | (C) Circumference of circle = 44 m |

If the height of X is greater than the height of Y, which of the following matches are correct?

Select the correct combination:

(a) (i) Only A, (ii) Either B or C, (iii) Only A

(b) (i) Either B or C, (ii) Only A, (iii) Only A, either B or C

(c) (i) Only B, (ii) Only A, (iii) Only A

(d) (i) Only C, (ii) Only B, (iii) Only B

(e) None of these

Accepted Answer

**Solution:**

1. Let the height of cone X be $h_x$ and the height of cylinder Y be $h_y$.

2. Given volumes:
   - Volume of cone $X = 1232 	ext{ m}^3$
   - Volume of cylinder $Y = 1848 	ext{ m}^3$

3. Possible radius values from Column II are 7 m (B) and 14 m (A).

4. For cylinder Y:
   - If radius $r = 7$ m, height $h_y = \frac{	ext{Volume}}{\pi r^2} = \frac{1848}{\frac{22}{7} 	imes 7^2} = 12 	ext{ m}$
   - If radius $r = 14$ m, height $h_y = \frac{1848}{\frac{22}{7} 	imes 14^2} = 3 	ext{ m}$

5. For cone X:
   - Volume formula: $V = \frac{1}{3} \pi r^2 h_x = 1232$
   - Using $r = 7$ m, $h_x = \frac{3 	imes 1232}{\pi 	imes 7^2} = 10 	ext{ m}$
   - Using $r = 14$ m, $h_x$ becomes negative (not possible), so discard this.

6. Comparing heights:
   - For $r = 7$ m, $h_x = 10$ m and $h_y = 12$ m (height of X is less than Y)
   - For $r = 14$ m, $h_x$ invalid
   - For $r = 7$ m (Y), $h_y = 12$ m; for $r = 14$ m (Y), $h_y = 3$ m

7. To satisfy $h_x > h_y$, height of Y must be 3 m (radius 14 m), and height of X is 10 m (radius 7 m).

8. For the square inscribed in circle:
   - Circumference $= 44$ m (C)
   - Radius of circle $= \frac{44}{2\pi} = 7$ m (matches B)

**Therefore, the correct matching is:**

- (i) X = Cone: Either B or C
- (ii) Y = Cylinder: Only A
- (iii) S = Square inscribed in circle: Only A or either B or C

**Answer:** (b) (i) Either B or C, (ii) Only A, (iii) Only A, either B or C

Answer

Answer

Answer