Unit Test: Surface Area & Volumes

Time: 1 hour
M.M. 30 
Attempt all questions. 
Question numbers 1 to 5 carry 1 mark each. 
Question numbers 6 to 8 carry 2 marks each. 
Question numbers 9 to 11 carry 3 marks each. 
Question numbers 12 & 13 carry 5 marks each.

Q1. What is the curved surface area of a right circular cone? (1 Mark)
(a) πr²
(b) πrl
(c) πr(l + r)
(d) 2πrl

Q2. What is the total surface area of a hemisphere? (1 Mark)
(a) 2πr²
(b) 3πr²
(c) 4πr²
(d) πr²

3. The volume of a cone is one-third the volume of a cylinder with the same: (1 Mark)
(a) Height only
(b) Radius only
(c) Height and radius
(d) Slant height

Q4. The surface area of a sphere of radius r is: (1 Mark)
(a) 2πr²
(b) 3πr²
(c) 4πr²
(d) πr²

^{Q5. The slant height of a cone is denoted by: (1 Mark)
(a) h
(b) r
(c) l 
(d) d}

^{Q6. Find the curved surface area of a cone with base diameter 7 cm and slant height 8 cm. (Use π = 22/7) (2 Mark)}

^{Q7. Calculate the surface area of a sphere with diameter 14 cm. (Use π = 22/7) (2 Mark)}

^{Q8. Find the curved surface area of a hemisphere with radius 10.5 cm. (Use π = 22/7) (2 Mark)}

^{Q9. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m. (3 Mark)}

^{Q10. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs.210 per 100 sq.m. (3 Mark)}

^{Q11. The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding. (3 Mark)}

^{Q12. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite. (5 Mark)}

^{Q13. A spherical ball is divided into two equal halves. Given that the curved surface area of each half is 56.57 cm, what will be the volume of the spherical ball? (5 Mark)}