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Surface Areas & Volumes — Chapter Test

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Q1
A conical heap of sand has base radius 12 m and height 5 m (π = 22/7). Its slant height is:
l = √(12² + 5²) = √169 = 13 m.
Q2
The surface area of a sphere of radius 7 cm (π = 22/7) is:
7
SA = 4πr² = 4 × 22/7 × 49 = 616 cm².
Q3
The curved surface area of a hemisphere of radius 7 cm (π = 22/7) is:
7
CSA = 2πr² = 2 × 22/7 × 49 = 308 cm².
Q4
The total surface area of a cuboid 12 cm × 10 cm × 8 cm is:
TSA = 2(lb + bh + hl) = 2(120 + 80 + 96) = 592 cm².
Q5
A cylinder, a cone and a hemisphere have the same radius and the cone and cylinder have height equal to the radius. The total volume is:
5 m12 ml
πr³ (cylinder) + ⅓πr³ (cone) + ⅔πr³ (hemisphere) = 2πr³.
Q6
A solid sphere has the same radius as a hemisphere. The sphere's volume is the hemisphere's volume times:
Sphere (4/3)πr³ is twice the hemisphere (2/3)πr³.
Q7
The volume of a cuboid 12 cm × 10 cm × 8 cm is:
12810
Volume = lbh = 12 × 10 × 8 = 960 cm³.
Q8
A cone has radius 7 cm and height 24 cm. Its slant height is:
247l
l = √(7² + 24²) = √625 = 25 cm.
Q9
If two solids have equal volumes but different shapes, then their surface areas are:
7 m25 m
Equal volume does not force equal surface area.
Q10
The volume of a cone of radius 7 cm and height 24 cm (π = 22/7) is:
725
Volume = ⅓πr²h = ⅓ × 22/7 × 49 × 24 = 1232 cm³.
Q11
A toy is a cone of radius r and height r mounted on a hemisphere of radius r. Its volume is:
0.7 m2 m
Cone ⅓πr³ plus hemisphere ⅔πr³ gives πr³.
Q12
A closed cylindrical can of radius 7 cm and height 10 cm needs a label covering its curved surface (π = 22/7). The label area is:
246l
CSA = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².
Q13
An ice-cream cone topped with a hemispherical scoop is an example of a:
It combines a cone and a hemisphere.
Q14
A frustum can be seen as a large cone with a smaller similar cone removed from its:
2.8 m1.5 m2 m
A frustum is the cone with the top (a smaller similar cone) cut off.
Q15
A cylindrical pillar of radius 0.5 m and height 7 m is to be painted on its curved surface (π = 22/7). The area to paint is:
CSA = 2πrh = 2 × 22/7 × 0.5 × 7 = 22 m².
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