✓ Board-verified
Mathematics · 2026 · 4 marks
CBSE 2026 · Region 5 · Set 2 · Q38
A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter 7 cm is latched…
A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter $\displaystyle 7$ cm is latched with a very thin rod. (Ignore the rod while making calculations.)
Dimensions of the cuboid are $\displaystyle 24$ cm × $\displaystyle 12$ cm × $\displaystyle 17$ cm.
(i)
Find the surface area of the bulb.
(ii)
What could be the maximum diameter of the bulb if at least $\displaystyle 1$ cm space is left from each side ?
(iii)
(a)
Find the area of the fabric used if there is a fold of $\displaystyle 2$ cm on top and bottom edges.
OR
(b)
Find the space available inside the lamp.
Marking-scheme solution
(i) Surface area of the bulb \(\displaystyle =4 \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}=154 \mathrm{~cm}^{2}\)
(ii) Maximum diameter of the bulb = Minimum side length - $\displaystyle 2$ cm
\[\text { = } 12-2=10 \mathrm{~cm}
\]
(iii)(a)
With $\displaystyle 2$ cm extra cloth for top and bottom edges,
new dimensions are $\displaystyle 24$ cm × $\displaystyle 12$ cm × $\displaystyle 21$ cm
Area of fabric used \(\displaystyle =2 \times 21 \times(24+12)=1512 \mathrm{~cm}^{2}\)
\[\text { (iii) (b)Space available } \begin{aligned}
= & 24 \times 12 \times 17-\frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} \\
& =4896-\frac{539}{3} \\
& =\frac{14149}{3} \mathrm{~cm}^{3} \text { or } 4716.3 \mathrm{~cm}^{3} \text { (approx.) }
\end{aligned}
\]
All Surface Areas and Volumes questions2026 question paperNCERT solutions: Surface Areas and VolumesPractice Surface Areas and Volumes →
More from Surface Areas and Volumes
- A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 m^2. Outer surface area of the tent is2026
- What is the total surface area of a solid hemisphere of diameter 'd'?2023
- On the day of her examination, Riya sharpened her pencil from both ends as shown below: The diameter of the cylindrical and conical part of the…2025
- The inner and outer radii of a hollow cylinder surmounted on a hollow hemisphere of same radii are 3 cm and 4 cm respectively. If height of the…2024
- The total surface area of a solid hemisphere of diameter ' 2 d ' is:2026
- From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area…2022
- A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the…2023
- 1000 small thermocol balls of radius 0•5 cm are kept in a spherical balloon of radius 20 cm. Find the volume of air in the balloon.2026
CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.