CBSE 2025 · Region 4 · Set 2 · Q35 · 5 marks
In order to provide shelter to flood victims, a shed was constructed using tin sheets which is in the form of cuboid surmounted by a half cylinder as shown below :
The length, breadth and height of cuboidal portion are $\displaystyle 10$ m, $\displaystyle 7$ m and $\displaystyle 3$ m respectively. The diameter of the cylindrical portion is $\displaystyle 7$ m . Find the cost of tin sheets required to make the shed at the rate of ₹ $\displaystyle 70$ per square metre, given that the shed is open from the front side and closed from the back side.
The length, breadth and height of cuboidal portion are $\displaystyle 10$ m, $\displaystyle 7$ m and $\displaystyle 3$ m respectively. The diameter of the cylindrical portion is $\displaystyle 7$ m . Find the cost of tin sheets required to make the shed at the rate of ₹ $\displaystyle 70$ per square metre, given that the shed is open from the front side and closed from the back side.Marking-scheme solution
Area of the sheet required for the shed
= (lateral surface area of the cuboid - front area) \(\displaystyle +\frac{1}{2}\) CSA of cylinder + area of semicircle
\[\begin{aligned}
& =[2 \times(10+7) \times 3-7 \times 3]+\frac{1}{2} \times 2 \times \frac{22}{7} \times \frac{7}{2} \times 10+\frac{1}{2} \times \frac{22}{7} \times\left(\frac{7}{2}\right)^{2} \\
& =\frac{841}{4} \mathrm{~m}^{2}
\end{aligned}
\]
Cost of sheet \(\displaystyle =\frac{841}{4} \times 70=₹ 14717.50\)
Surface Areas and VolumesSurface Area of a Combination of SolidsApplylong_answerhard
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.