A right circular cylinder of maximum volume is cut from a solid cube of edge 14cm. The total surface area of the cylinder is
- A924cm
2 - B1134cm
2 - C2464cm
2 - D616cm
2
Solution & Step-by-step Explanation
When a right circular cylinder of maximum possible volume is carved out from a solid cube of side length a=14cm:
The height (h) of the cylinder will be equal to the edge length of the cube:
h=a=14cm
The base diameter of the cylinder will also equal the edge length of the cube, meaning its radius (r) is half the side length:
r=
2
a
=
2
14
=7cm
The mathematical formula for the Total Surface Area (TSA) of a cylinder is:
TSA=2πr(r+h)
Using π≈
7
22
, substitute the values into the formula:
TSA=2×
7
22
×7×(7+14)
TSA=2×22×21
TSA=44×21=924cm
2
The height (h) of the cylinder will be equal to the edge length of the cube:
h=a=14cm
The base diameter of the cylinder will also equal the edge length of the cube, meaning its radius (r) is half the side length:
r=
2
a
=
2
14
=7cm
The mathematical formula for the Total Surface Area (TSA) of a cylinder is:
TSA=2πr(r+h)
Using π≈
7
22
, substitute the values into the formula:
TSA=2×
7
22
×7×(7+14)
TSA=2×22×21
TSA=44×21=924cm
2