SOLUTION: A square prism in inscribed in a cylinder. The prism has a height of 12 inches and the cylinder has a radius of 5 inches. What's the lateral area and surface area of the prism and
Algebra.Com
Question 622471: A square prism in inscribed in a cylinder. The prism has a height of 12 inches and the cylinder has a radius of 5 inches. What's the lateral area and surface area of the prism and the cylinder
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I assume that from above you just see the bases of the prism and the cylinder, looking like a square inscribed in a circle, like this:
The diameter of the circle is 10 inches, the length of the diagonal of the square.
Two sides of the square, of length x inches, form a right triangle with the diagonal for a hypotenuse, so
--> --> -->
The area of the circle (with radius 5) is square inches.
That circle is one of the two congruent (equal) bases of the cylinder.
The circumference is inches, and the lateral area of the cylinder is that times the height, or
square inches.
So the total surface area of the cylinder is
square inches.
The area of the square is square inches.
That square is one of the two congruent (equal) bases of the prism.
The perimeter of the square is inches, and the lateral area of the prism is that times the height, or
square inches.
So the total surface area of the cylinder is
square inches.
RELATED QUESTIONS
A square prism is inscribed in a cylinder. The prism has a height of 12 inches and the... (answered by KMST)
The altitude of a right circular cylinder and the radius of its base are each 12 inches... (answered by CPhill)
A cylinder has a volume of 32 in^3. If the height of the cylinder is 5 inches more than... (answered by josgarithmetic)
A cylinder has a radius of 4 inches and a height of 16 inches. What is the volume of the... (answered by Alan3354)
if a cylinder has a radius of 12 inches and a volume of 13564.8 cubic inches. what is the (answered by math problem solving)
A rectangular prism has a base area of 400 square inches. The volume of the prism is 2 ,... (answered by KMST)
A right, regular triangular prism has a circular cylinder inscribed in it (see figure to... (answered by greenestamps)
Find the volume of the largest cylinder that can be inscribed in a right circular cone of (answered by solver91311)