One Rectangular plate with length 8 inches breadth 11 inches and 2 inches thickness is there. What is the length of the circular rod with diameter 8 inches and equal to volume of rectangular plate ?a)3.5 INCHESb)3.1INCHESc)2.5 INCHESd)3.2INCHESCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Volume of rectangular plate = Volume of circular Rod

l*b*h =

πr^2H

11*8*2 = 22/7*4^2*H

H = 3.5 inches ans

Answer

To find the length of the circular rod, we need to calculate the volume of the rectangular plate and then use that volume to find the length of the rod.

Step 1: Calculate the volume of the rectangular plate
The volume of a rectangular plate is given by the formula: Volume = Length * Breadth * Thickness

Given that the length is 8 inches, breadth is 11 inches, and thickness is 2 inches, we can substitute these values into the formula:
Volume = 8 inches * 11 inches * 2 inches
Volume = 176 cubic inches

Step 2: Calculate the volume of the circular rod
The volume of a cylinder (which is the shape of the circular rod) is given by the formula: Volume = π * (radius)^2 * height

Given that the diameter of the circular rod is 8 inches, the radius is half of the diameter, which is 4 inches. The height of the rod is unknown, so let's assume it to be 'h'.
Volume = π * (4 inches)^2 * h
Volume = 16πh cubic inches

Step 3: Equate the volumes of the rectangular plate and the circular rod
Since the volume of the circular rod is equal to the volume of the rectangular plate, we can equate the two values:
16πh = 176

Step 4: Solve for 'h'
Divide both sides of the equation by 16π:
h = 176 / (16π)
h ≈ 3.5 inches

Therefore, the length of the circular rod is approximately 3.5 inches. Hence, option A is the correct answer.

Similar Quant Doubts

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and resolidified in the form of a rod of 8 inches diameter. The length of such a rod, in inches, is

A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 18 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many cm will the water level rise?

A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 14 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many centi metre will the water level rise?

Length of a rectangular field is increased by 10 meters and breadth is decreased by 4 meters, area of the field remains unchanged. If the length decreased by 5 meters and breadth is increased by 7 meters, again the area remains unchanged. Find the length and breadth of the rectangular field.

Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted is

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company