✓ Board-verified
Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 1 · Q11
(a) 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…
(a)
From a solid cylinder of height $\displaystyle 30$ cm and radius $\displaystyle 7$ cm, a conical cavity of height $\displaystyle 24$ cm and same radius is hollowed out. Find the total surface area of the remaining solid.
OR
(b)
Water in a canal, $\displaystyle 8$ m wide and $\displaystyle 6$ m deep, is flowing with a speed of $\displaystyle 12$ km/hour. How much area will it irrigate in one hour, if $\displaystyle 0.05$ m of standing water is required ?
Marking-scheme solution
\[l=\sqrt{576+49}=25 \mathrm{~cm}
\]
\[\begin{aligned}
\mathrm{TSA} & =2 \pi r h+\pi r^{2}+\pi r l \\
& =\frac{22}{7} \times 7[60+7+25] \\
& =2024 \mathrm{~cm}^{2}
\end{aligned}
\]OrDistance covered by water in $\displaystyle 1 \mathrm{hr}=12000 \mathrm{~m}$
∴ Volume of water flown in $\displaystyle 1$ hr
\[=8 \times 6 \times 12000 \mathrm{~m}^{3}
\]Hence area of field $\displaystyle \times 0 \cdot 05=8 \times 6 \times 12000$
\[\Rightarrow \quad \text { Area of field }=1152 \times 10^{4} \mathrm{~m}^{2} \text { or } 11520000 \mathrm{~m}^{2}
\]
\[\begin{aligned}
\mathrm{TSA} & =2 \pi r h+\pi r^{2}+\pi r l \\
& =\frac{22}{7} \times 7[60+7+25] \\
& =2024 \mathrm{~cm}^{2}
\end{aligned}
\]OrDistance covered by water in $\displaystyle 1 \mathrm{hr}=12000 \mathrm{~m}$
∴ Volume of water flown in $\displaystyle 1$ hr
\[=8 \times 6 \times 12000 \mathrm{~m}^{3}
\]Hence area of field $\displaystyle \times 0 \cdot 05=8 \times 6 \times 12000$
\[\Rightarrow \quad \text { Area of field }=1152 \times 10^{4} \mathrm{~m}^{2} \text { or } 11520000 \mathrm{~m}^{2}
\]All Surface Areas and Volumes questions2022 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 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.