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


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