Question 16 A rectangular prism is shown in the following di

Question 16 A rectangular prism is shown in the following diagram. The lengths of the sides, in centimetres, are represented by a, b and c. The prism is cut through the middle along the plane of the quadrilateral HCDF Which of the following statements is/are true? A. Consider the solid with base the rectangle ABCD: and sides the rectangles ABHF and HCDF, and the triangles AFD and BHC. The volume of this solid is equal to abx C. If each of the lengths a, b and e is doubled, the ratio of the volume of bigger prism thus formed to the volume of the original prism will be 2:1 1. Only A 2. Only B 58 MATO511/101/0/2018 3. Only C 4. Only A and B 5. Only B and C Question 17 Which of the following statements is/are true? A. Suppose a sphere has a diameter of 10 cm. Suppose the radius of a closed right circular cylinder is the same as the radius of the sphere and its height is double its radius. The ratio of the surface area of the sphere to that of the cylinder is 2:3. If the diameter and height of a right circular cone are equal then the lateral surface area of the cone is If the diagonals of a quadrilateral intersect at right angles the quadrilateral must be a square or a rhombus or a kite. B. (radius)2 C. 1. Only A 2. Only B 3. Only C 4. Only A and C 5. A, B and C Question 18 Consider a photograph with dimensions 10 cm by 8 cm. Which of the following statements is/are true? A. If the photograph is enlarged by a scale factor of 3 it will fit onto a piece of paper that measures 30 cm by 20 em If it is enlarged by a scale factor of 2,5 it will fit onto a 30 em by 20 em piece of paper with no space left on the sides and 2,5 cm above and below the photograph. If it is reduced by a scale factor of 0,75 then eight such photographs will cover the 30 cm by 20 cm page exactly B. C. 1. Only A 2. Only B 3. Only C 4. Only B and C 5. A, B and C

Solution

16)

A is correct since basically rectangle HCDF divides the whole cuboid into two equal volumes

The volume of the whole cuboid is abc hence the volume of the figure described in option A

is abc/2

B is correct since BC=GH=b ,GC = c

Applying Pythagorean theorem in triangle CGH we get HC² = b² + c²

C is incorrect since when a,b,c are doubled the new volume becomes 2a x 2b x 2c = 8abc = 8 x volume of previous cuboid

17)

A)

The radius of the sphere, the cylinder is 5 cm height of the cylinder is 10 cm from question

Surface area of sphere is 4 x p x r² , of cylinder is 2 x p x r x h + 2 x p x r ²

Ratio of them is 4 x p x r² / (2 x p x r x h + 2 x p x r ²)=2r/(h+r)=2x5/15=2/3

Therefore it is true

B)

Given diameter equal to height of cone which is equal to 2xradius=2r

Lateral surface area = p x r x sqrt(r²+h²) =p x r x sqrt(5) x r= pxsqrt(5)xr²

Hence the option is true

C)

The perpendicular intersection of diagonals in the quadrilateral is a unique property of kites, rhombus, square

Hence the statement is true