Three identical cylinders are inscribed within a rectangular solid, shown above from the top. If the length of the rectangular solid is 4 feet and the height (not shown) is 2 feet, what is the volume of the rectangular solid?a)4(2 + /2)b)4(2 + )c)8(2 + 2)d)8(2 + 3)e)12(1 + 3)Correct answer is option 'D'. Can you explain this answer?

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a)
4(2 + π/2)
b)
4(2 + π)
c)
8(2 + 2π)
d)
8(2 + √3)
e)
12(1 + √3)

Correct answer is option 'D'. Can you explain this answer?

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Test: Rectangular Solids- 1

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Three identical cylinders are inscribed within a rectangular solid, sh...

Step 1: Question statement and Inferences

For the volume of the rectangular solid, you need the length, width, and height. You already have the length and the height, 4 and 2, respectively. Use the cylinders to calculate the width.

Step 2: Finding required values

Draw an equilateral triangle where each vertex is the center of one circle.

If the length of the rectangle is 4, the diameter of each circle is 2, and the radius is 1. The triangle is equilateral with a base of 2.

To find the height of the triangle, cut it in half as shown below, into two 30-60-90 triangles. With a hypotenuse of 2 and a base of 1 (half the side is the base), use the Pythagorean Theorem to find the third side, which is the height:

Add this height of the triangle to the circle radii above and below it for a rectangular solid width of (2 + √3)

Step 3: Calculating the final answer

By multiplying the length and height by the newly found width, we get:

The volume of the solid = 4*2*(2 + √3)

= 8*(2 + √3)

Answer: Option (D)

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Three identical cylinders are inscribed within a rectangular solid, shown above from the top. If the length of the rectangular solid is 4 feet and the height (not shown) is 2 feet, what is the volume of the rectangular solid?a)4(2 + π/2)b)4(2 + π)c)8(2 + 2π)d)8(2 + √3)e)12(1 + √3)Correct answer is option 'D'. Can you explain this answer?

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