Chapter 12 · Surface Areas and Volumes

NCERT Exemplar Class 10 Maths Exercise 12.2

All 8 questions of NCERT Exemplar Class 10 Maths Exercise 12.2 (Surface Areas and Volumes), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Two identical solid hemispheres of equal base ​radius $r$ cm are stuck ​together along their ​bases. The ​total ​surface area of ​the combination is $6\pi r^2$.
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   False

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2. Q2
   Write 'True' or 'False' ​and justify ​your answer: A solid ​cylinder of radius $r$ and height $h$ is placed over another ​cylinder ​of same height ​and radius. ​The total surface area of the shape ​so formed is $4\pi rh+4\pi r^2$.
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   False

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3. Q3
   A solid cone of radius $r$ and ​height $h$ is placed over a ​solid cylinder having ​same ​base ​radius and height as that ​of a cone. The total surface area ​of the combined ​solid is $\pi r\left[\sqrt{r^2+h^2}+3r+2h\right]$.
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   False

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4. Q4
   A solid ball is ​exactly fitted inside the cubical box of side $a$. ​The volume of the ​ball ​is $\frac{4}{3}\pi a^3$. Write 'True' ​or ​'False' and justify ​your answer.
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   False. The ball's radius is $a/2$, so its volume is $\frac{4}{3}\pi (a/2{)}^3=\frac{\pi a^3}{6}$, not $\frac{4}{3}\pi a^3$.

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5. Q5
   State ​whether the following statement is true or false and justify: ​The volume of the frustum of a ​cone ​is $\frac{1}{3}\pi h[r_1^2+r_2^2-r_1{r}_2]$, where $h$ is the ​vertical height of ​the ​frustum and $r_1,r_2$ are the radii of ​the ends.
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   False

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6. Q6
   The capacity of a cylindrical vessel with ​a hemispherical ​portion raised ​upward ​at the ​bottom ​as ​shown in the Fig. 12.7 ​is $\frac{\pi r^2}{3}[3h-2r]$.

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   Capacity $=\frac{\pi r^2}{3}(3h-2r)$, which is the required result.

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7. Q7
   The curved surface area of ​a frustum ​of ​a cone is $\pi l(r_1+r_2)$, where $l=\sqrt{h^2+(r_1+r_2{)}^2}$, $r_1$ and $r_2$ are the ​radii of ​the ​two ends of the frustum and $h$ is the ​vertical height.
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   False

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8. Q8
   An open metallic ​bucket is in the shape of a frustum of a cone, mounted on a hollow ​cylindrical base made of ​the same metallic sheet. The surface area ​of ​the metallic sheet ​used ​is equal to curved surface area of frustum of a cone + area of circular ​base + curved surface area of cylinder.
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   True

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