Final answer:
The amount of metal sheet needed to make a cylindrical pipe 10 cm long and with a 7 cm radius is found by calculating the lateral surface area. Using the formula A = 2πrh, the answer is 140π cm², which is option (a).
Step-by-step explanation:
The question is asking to determine the amount of metal sheet required to make a cylindrical pipe which has a length of 10 centimeters and a radius of 7 centimeters.
To find the metal sheet required, we calculate the surface area of the cylindrical part of the pipe which is the lateral surface area, as the ends of the pipe are not covered by metal sheet. The formula for the lateral surface area (A) of a cylinder is A = 2πrh, where r is the radius, and h is the height or length of the cylinder.
Now let's put the values into the formula: A = 2π(7 cm)(10 cm) = 140π cm². Thus, the correct amount of metal sheet needed is 140π cm², which corresponds to option (a).