Answer to Question #93282 in Geometry for bongani

Question

Which of the following statements is/are true?
A. Suppose a sphere has a diameter of 10 cm. Suppose the height of a closed right circular cylinderis double its radius, and that its radius is the same as the radius of the sphere. The ratio of the surface area of the sphere to that of the cylinder is 2 : 3.
B. If the diameter and height of a right circular cone are equal then the lateral surface area of the cone is √ 5πr2 , where the radius is r. (Note: Lateral surface area of cone is the area of the sides only.)
C. If the diagonals of a quadrilateral intersect at right angles the quadrilateral must be a square or a rhombus or a kite.
1. Only A 2. Only B 3. Only C
4. Only A and C 5. A, B and C

Answer 1

A) radius of sphere = 10/2 = 5 hence surface area of sphere = 4 π(5)2 =100 π

radius of cylinder r = 5 , height of cylinder h = 2r = 2(5) =10

hence surface area of cylinder = 2π r2 +2 π rh = 2 π 52 + 2π (5)(10) = 150 π

the required ratio = (100 π)/ ( 150π) = 2/3

hence the given statement is true.

B) height h = diameter = 2r

slant height l =$\sqrt{r^{2}+ h^{2}}$ =$\sqrt{r^{2}+ (2r)^{2}}$ =$\sqrt{5}$ r

lateral surface area = π rl = π r $\sqrt{5}$ r =$\sqrt{5}$ π r²

hence the given statement is true.

C) Of all the quadrilaterals , diagonals of only squares , rhombuses and kites intersect at right angles.

Hence A ,B ,C all are correct hence the option 5 is correct.