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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 2 · Set 1 · Q38
On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream…
On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you.
Based on the information given above, answer the following questions :
(i)
Find the length of the diagonal of Rubik's cube if each edge measures $\displaystyle 6$ cm.
(ii)
Find the volume of Rubik's cube if the length of the edge is $\displaystyle 7$ cm.
(iii)
(a)
What is the curved surface area of hemisphere (ice-cream) if the base radius is $\displaystyle 7$ cm ?
OR
(b)
If two cubes of edges $\displaystyle 4$ cm are joined end-to-end, then find the surface area of the resulting cuboid.
Marking-scheme solution
(i)
Length of diagonal of cube \(\displaystyle =\sqrt{3} \times\) side
\[=6 \sqrt{3} \mathrm{~cm}
\]
\(\displaystyle =6 \sqrt{3} \mathrm{~cm}\)
(ii)
Volume of Rubik's cube \(\displaystyle =(7)^{3}\)
\(\displaystyle =343 \mathrm{~cm}^{3}\)
(iii)(a)
CSA of hemisphere \(\displaystyle =2 \times \frac{22}{7} \times 7 \times 7\)
\(\displaystyle =308 \mathrm{~cm}^{2}\)
(iii)(b)
Surface area of resulting cuboid \(\displaystyle =5(4)^{2}+5(4)^{2}\)
\(\displaystyle =160 \mathrm{~cm}^{2}\)
ALTERNATE SOLUTION :
(iii)(b)
Surface area of resulting cuboid \(\displaystyle =2(8 \times 4+4 \times 4+8 \times 4)\)
\(\displaystyle =160 \mathrm{~cm}^{2}\)
All Surface Areas and Volumes questions2026 question paperNCERT solutions: Surface Areas and VolumesPractice Surface Areas and Volumes →
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