Chapter 12 · Surface Areas and Volumes

NCERT Class 10 Maths Exercise 12.1

All 9 questions of NCERT Class 10 Maths Exercise 12.1 (Surface Areas and Volumes), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   2 ​cubes each ​of volume ​64 cm^3 are joined end to end. Find the ​surface ​area of the ​resulting ​cuboid.
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   Surface area of the resulting cuboid $=160$ cm².

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2. Q2
   A vessel is in the ​form of ​a ​hollow ​hemisphere mounted by a hollow cylinder. The diameter ​of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the ​inner surface ​area of ​the vessel.
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   Inner surface area $=572$ cm².

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3. Q3
   A toy ​is in the ​form of ​a cone of radius 3.5 cm mounted on a ​hemisphere ​of same radius. The total height of the toy ​is 15.5 cm. Find the total surface area of ​the toy.
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   Total surface area of the toy $=214.5$ cm².

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4. Q4
   A cubical block ​of side ​7 cm is ​surmounted by a hemisphere. ​What is ​the greatest ​diameter the hemisphere can have? Find ​the surface area ​of the solid.
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   Greatest diameter $=7$ cm; surface area $=332.5$ cm².

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5. Q5
   A hemispherical depression is cut out from one face ​of a cubical wooden block such that the diameter $l$ of the hemisphere ​is equal to the edge of the ​cube. Determine the surface ​area of ​the ​remaining ​solid.
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   Surface area $=6l^2+\frac{\pi l^2}{4}=\frac{l^2}{4}(24+\pi )$ square units.

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6. Q6
   A medicine capsule is in the shape of a ​cylinder with two hemispheres stuck to each of ​its ends ​(see Fig. 12.10). The length ​of the entire capsule ​is 14 mm and the diameter of the capsule is ​5 mm. ​Find its surface area.

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   Surface area $=220$ mm${}^2$.

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7. Q7
   A tent is in the shape of a cylinder surmounted by a conical top. If the height and ​diameter of ​the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the ​top is ​2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per ​m^2. ​(Note that ​the base ​of the tent will not be covered with canvas.)
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   Canvas area $=44$ m²; cost $=$ Rs $22000$.

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8. Q8
   From a ​solid cylinder whose height is $2.4$ cm and diameter $1.4$ cm, a conical cavity ​of the same ​height and same diameter is hollowed ​out. ​Find the total surface area ​of the remaining solid to the nearest ​cm${}^2$.
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   Total surface area $=17.6$ cm² $\approx 18$ cm².

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9. Q9
   A ​wooden article was made by scooping out a hemisphere from each ​end of a ​solid cylinder, ​as shown in Fig. 12.11. If the height of the cylinder is 10 cm, ​and ​its base is of radius 3.5 cm, find the total surface area of the article.

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   Total surface area $=374$ cm${}^2$.

   Step-by-step solution →