MATH SOLVE

2 months ago

Q:
# "Anik" is the name of a series of Canadian communications satellites. The first Anik shown here, was launched in 1972. It was a cylindrical shape, 3.5 m high and 190 cm in diameter. All satellites are wrapped with insulation because the instruments inside will not work if they become too cold or hot. What was the approximate area of the insulation used to wrap the first Anik?

Accepted Solution

A:

The surface area would be 26.5487 m².

The surface area of a cylinder is equal to the area of the circles at both ends, added to the area of the rectangular portion in the middle. The rectangle in the middle has a width equal to the circumference of the circle and a length equal to the height of the cylinder.

The circumference of a circle is given by C = πd, and the area of the circles is given by A=πr².

Since the height is in meters, we will convert it to cm. 3.5 m = 350 cm.

The diameter is 190 cm, so the radius is 190/2 = 95 cm.

This gives us:

SA = 3.14(190)(350)+2(3.14)(95)²

= 208810 + 56677 = 265487 cm² = 26.5487 m²

The surface area of a cylinder is equal to the area of the circles at both ends, added to the area of the rectangular portion in the middle. The rectangle in the middle has a width equal to the circumference of the circle and a length equal to the height of the cylinder.

The circumference of a circle is given by C = πd, and the area of the circles is given by A=πr².

Since the height is in meters, we will convert it to cm. 3.5 m = 350 cm.

The diameter is 190 cm, so the radius is 190/2 = 95 cm.

This gives us:

SA = 3.14(190)(350)+2(3.14)(95)²

= 208810 + 56677 = 265487 cm² = 26.5487 m²