cylindrical solid whose radius and height are equal has a surface area of 154cm2. Calculate its diameter, correct to 2 decimal places. (Take = 3.142)
SA=2(PI*r^2)+PI*r*h
solve for r (r and h are equal)
SA=r^2(2PI+PI)
r=Sqrt (SA/3Pi) and thendiameter is 2*radius.
To find the diameter of the cylindrical solid, we need to first find its radius.
Let's assume the radius of the cylindrical solid is denoted by r.
The total surface area of a cylindrical solid is given by the formula:
Surface Area = 2πr(r + h),
where h is the height of the cylindrical solid.
Given that the radius and height are equal, we can rewrite the formula as:
Surface Area = 2πr(r + r)
Surface Area = 2πr(2r)
Surface Area = 4πr^2
Now, we can substitute the given value of surface area and solve for r:
154cm^2 = 4πr^2
Dividing both sides of the equation by 4π:
154 / (4π) = r^2
Simplifying the right side of the equation:
r^2 = 154 / (4π)
Calculating the value of r:
r^2 ≈ 12.26
Taking the square root of both sides:
r ≈ √12.26
r ≈ 3.50 (rounded to 2 decimal places)
The diameter (d) of the cylindrical solid is twice the radius (d = 2r). Substituting the value of the radius:
d ≈ 2 * 3.50
d ≈ 7.00 (rounded to 2 decimal places)
Therefore, the diameter of the cylindrical solid is approximately 7.00 cm.
To solve this question, we can start by using the formula for the surface area of a cylinder:
Surface Area = 2πrh + 2πr²
In this case, we know that the radius (r) and the height (h) of the cylinder are equal. Let's represent this value as D, which stands for diameter.
Since the diameter is equal to the radius multiplied by 2 (D = 2r), we can rewrite the formula as:
Surface Area = 2π(D/2)(D/2) + 2π(D/2)²
Simplifying the equation gives us:
Surface Area = π(D²/4) + π(D²/4)
Multiplying the common denominator (4) on both terms, we have:
Surface Area = π(D² + D²)/4
Since the surface area is known to be 154 cm², we can substitute this value into the equation:
154 = π(D² + D²)/4
To solve for D, we need to rearrange the equation:
D² + D² = (154 * 4) / π
2D² = (616 / π)
D² = (616 / π) / 2
D² = 308 / π
D ≈ √(308 / π)
Now, let's calculate the value of D using the given approximation of π as 3.142:
D ≈ √(308 / 3.142)
D ≈ √(98.038)
D ≈ 9.90
Therefore, the diameter of the cylindrical solid is approximately 9.90 cm when rounded to 2 decimal places.