12.2.2 Solid Geometry (II), PT3 Focus Practice


12.2.2 Solid Geometry (II), PT3 Focus Practice

Question 5:
Sphere below has a surface area of 221.76 cm2.


Calculate its radius.
( π = 22 7 )

Solution:
Surface area of sphere = 4πr2
4 π r 2 = 221.76 4 × 22 7 × r 2 = 221.76 r 2 = 221.76 × 7 4 × 22 r 2 = 17.64 r = 17.64 r = 4.2 cm


Question 6:
Diagram below shows a right pyramid with a square base.

Given the height of the pyramid is 4 cm.
Calculate the total surface area, in cm2, of the right pyramid.

Solution:
h2 = 32 + 42
= 9 + 16
= 25
h = √25   = 5 cm2

Total surface area of the right pyramid
= Base area + 4 (Area of triangle)
= (6 × 6) + 4 × 4 (½ × 6 × 5)
= 36 + 60
= 96 cm2


Question 7:
Diagram below shows a prism.

Draw to full scale, the net of the prism on the grid in the answer space. The grid has equal squares with sides of 1 unit.

Solution:


12.2.1 Solid Geometry (II), PT3 Focus Practice


12.2.1 Solid Geometry (II), PT3 Focus Practice

Question 1:
Diagram below shows closed right cylinder.

Calculate the total surface area, in cm2, of the cylinder.  

( π = 22 7 )

Solution
:
Total surface area
= 2(πr2) + 2πrh
= ( 2 × 22 7 × 7 2 ) + ( 2 × 22 7 × 7 × 20 ) = 308 + 880 = 1188 c m 2



Question 2:
Diagram below shows a right prism with right-angled triangle ABC as its uniform cross section.
Calculate the total surface area, in cm2, of the prism.

Solution
:
A B = 5 2 3 2 = 25 9 = 16 = 4 c m

Total surface area
= 2 (½× 3 × 4) + (3 × 10) + (4 × 10) + (5 × 10)
= 12 + 30 + 40 + 50
= 132 cm2


Question 3:
Diagram below shows a right pyramid with a square base.

Calculate the total surface area, in cm2, of the right pyramid.  

Solution
:
h2= 102 – 62
   = 100 – 36
   = 64
= √64
   = 8cm

Total surface area of the right pyramid
= (12 × 12) + 4 × (½× 12 × 8)
= 144 + 192
= 336 cm2


Question 4:

The diagram shows a cone. The radius of its base is 3.5 cm and its slant height is 6 cm. Find the area of its curved surface.
( π= 22 7 )

Solution
:
Area of curved surface
= π × radius of base × slant height
= πrs
= 22 7 × 3.5 × 6 = 66 c m 2