Unit Test: Surface Areas and 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 number 12 & 13 carry 5 marks each.

Q1: Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is  (1 Mark)

(a) 12a²
(b) 10a²
(c) 8a²
(d) 11a²

Q2: A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter  (1 Mark)

(a) r cm 
(b) 2r cm 
(c) h cm 
(d) 2h cm

Q3: If we join two hemispheres of same radius along their bases, then we get a; (1 Mark)

(a) Cone
(b) Cylinder
(c) Sphere
(d) Cuboid

Q4: The radius of the top and bottom of a bucket of slant height 35 cm are 25 cm and 8 cm. The curved surface of the bucket is _________________________________. (1 Mark) 

Q5: If a cone is cut parallel to the base of it by a plane in two parts, then the shape of the top of the cone will be a: (1 Mark)

(a) Sphere
(b) Cube
(c) Cone itself
(d) Cylinder

Q6: 2 cubes each for the volume of 64 cm3 are joined end to end. Find out the surface area of the resulting cuboid. (2 Marks)

Q7: A cubical block of the side 7 cm is surmounted with a hemisphere. What is the greatest diameter the hemisphere could have? Find out the surface area of the solid. (2 Marks)

Q8: Two cones have their heights in the ratio of 1 : 3 as well as radii in the ratio of 3: 1. What is the ratio for their volumes? (2 Marks)

Q9: Water is flowing at the rate of 15 km/h passing through a pipe of the diameter of 14 cm into a cuboidal pond which is 50 m long and 44 m wide. At what time will the level for the water in the pond rise by 21 cm? (3 Marks)

Q10: A heap of rice is in the form for the cone of diameter of 9 m and height of 3.5 m. Find out the volume of the rice. How much canvas cloth is required to cover the heap only? (3 Marks)

Q11: Rasheed gets a playing top (lattu) as his birthday present, in which, surprisingly, he found no colour on it. He wanted to colour it with his crayons. The top is shaped as like a cone surmounted with a hemisphere. The entire top of 5 cm in height, as well as the diameter of the top, is 3.5 cm. Find out the area he has to colour. (Take π = 22/7) (3 Marks)

Q12: Water flows at the rate of 10m/minute and passes through a cylindrical pipe 5 mm in diameter. How long will it take to fill a conical vessel which has a diameter at the base is 40 cm and a depth of 24 cm? (5 Marks)

Q13: From a solid cylinder those height is 2.4 cm as well as diameter of 1.4 cm. A conical cavity for the same height as well as same diameter is hollowed out. Find out the total surface area of the remaining solid to the nearest cm². (5 Marks)

You can find the solutions of this Unit Test here: Unit Test (Solutions): Surface Areas and Volumes​