Series RTEQ.P. Code 16/0/0
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Unit test · Ch 12: Surface Areas and Volumes
Time allowed : 40 MinutesMaximum Marks : 20
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 11 questions. All questions are compulsory.
(ii)This question paper is divided into three sections – A, B and C.
(iii)In Section A, Question numbers 1 to 5 carry 1 mark each.
(iv)In Section B, Question numbers 6 to 8 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 9 to 11 are short answer (SA) type questions carrying 03 marks each.
(vi)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(vii)Use of calculators is not allowed.
SECTION A
This section comprises 5 questions of 1 mark each.
1.1
The volume of a cone is what fraction of the volume of a cylinder having the same base and height?
2.1
Find the length of the diagonal of a cuboid of dimensions 2 cm × 3 cm × 6 cm.
3.1
Find the slant height of a cone of base radius 5 cm and height 12 cm.
4.1
Find the total surface area of a solid hemisphere of radius 7 cm. (Use π = 22/7)
5.1
Find the curved surface area of a cylinder of radius 7 cm and height 10 cm. (Use π = 22/7)
SECTION B
This section comprises 3 very short answer (VSA) type questions of 2 marks each.
6.2
Find the volume of a cone of base radius 3 cm and height 7 cm. (Use π = 22/7)
7.2
A solid metal sphere of radius 6 cm is melted into 27 equal small spheres. Find the radius of each small sphere.
8.2
Two cubes, each of volume 8 cm³, are joined end to end. Find the total surface area of the resulting cuboid.
SECTION C
This section comprises 3 short answer (SA) type questions of 3 marks each.
9.3
A solid metal sphere of radius 10.5 cm is melted and recast into small cones, each of base radius 3.5 cm and height 3 cm. How many cones are made? (Use π = 22/7)
10.3
A solid is formed by a cone of height 4 cm placed on a hemisphere of radius 3 cm. Find its volume. (Use π = 3.14)
11.3
A capsule is a cylinder with a hemisphere at each end. Its total length is 25 cm and its diameter is 14 cm. Find its total surface area. (Use π = 22/7)
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