Answer to Question #92198 in Geometry for Masungulo

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 cylinder
is 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 the sphere r therefore area of the sphere:

$$S=4\pi r^2$$

circular cylinder:  radius= r, height= 2r therefore area of the cylinder:

$$S=2\pi rh+2\pi r^2$$ $$S=2\pi r2r+2\pi r^2=6\pi r^2$$

The ratio of the surface area of the sphere to that of the cylinder is 2 : 3.  A is true.

B. Circular cone: radius=r, diameter=2r, height=diameter=2r=h therefore area of the forming a cone:

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

Area of the cone

$$S=\pi rl=\sqrt{5}\pi r^2$$

B is true.

C.

Rhombus: Characterizations - a parallelogram in which the diagonals are perpendicular

(https://en.wikipedia.org/wiki/Rhombus)

Square: Characterizations -a rhombus with all angles equal

(https://en.wikipedia.org/wiki/Square)

in the simplest kites it is used geometrical figures such as square or rhombus. They are square shapes.

Kite.

Characterizations-One diagonal is the perpendicular bisector of the other diagonal

https://en.wikipedia.org/wiki/Kite_(geometry)

C is true.

Answer: option 5.