Question

A cylindrical vase has height 17 in. and radius 3 in. Find the exact surface area of the vase in terms of pi. Suppose a second vase has double the​ radius, but the same surface area. What is the height of this​ vase?

Answer 1

Answer: for first vase area = 120¶

For second vase height h = 4inches

Step-by-step explanation: surface area of cylinder is

A = 2¶r2 + 2¶rh = 2¶r(r + h)

Radius r = 3in

Height h = 17in

A = 3x2¶(3 +17) = 6¶(20)

A = 120¶

Suppose another vase has double the radius but the same surface area, then,

Radius r = 3x2 = 6inches

From A = 2¶r(r + h)

120¶ = 6x2¶(6 + h)

120 = 12(6 +h)

10 = 6 + h

h = 4inches