1. The radius of a cylinder is 5/6 its height. Find the total surface area of the cylinder if its volume is 150pi.
2. A prism and a cone have the same base area and the same height. The volume of the prism is 1. What is the volume of the cone?
3. A 288 degree circular sector with radius 15 is rolled to form a cone. Find the height of the cone.
4. The two bases of a right conical frustum have radii 12 and 9. The two bases are 4 units apart. Let the volume of the frustum be V (variable not roman numeral) cubic units and the total surface area of the frustum be A square units. Find V+A .
+128406 1. The radius of a cylinder is 5/6 its height. Find the total surface area of the cylinder if its volume is 150pi.
Vcylinder = pi ^r^2 * height
150 pi = pi ( 5/6 height)^2 * height
150 = (25/36) * height^3
150 * 36 / 25 = height^3
6 * 36 = height^3
216 = height^3
6 = height
(5/6)(6) = radius = 5
Surface area = pi * r^2 + 2pi * r * h = pi * 5^2 + 2pi (5)(6) =
25 pi + 60 pi =
85 pi units^2
+128406 2. A prism and a cone have the same base area and the same height. The volume of the prism is 1. What is the volume of the cone?
Cone volume = (1/3) base area * height = 1/3
+128406 3. A 288 degree circular sector with radius 15 is rolled to form a cone. Find the height of the cone.
15 will be the slant height of the cone
To find the cone's circumference....we have that
(288/360) * 2 pi * 15 = 24 pi
So...to find the radius of the cone, we have that
24 pi = 2 pi * radius
24 = 2 * radius
12 = radius
Using the Pythagorean Theorem the height is
sqrt ( 15^2 - 12^2 ) = sqrt (225 - 144) = sqrt (81) = 9
