Chapter 12 · Surface Areas and Volumes

NCERT Class 10 Maths Exercise 12.2

All 8 questions of NCERT 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
   A ​solid is in the shape of a ​cone ​standing ​on ​a hemisphere with both their radii being equal to $1$ cm and the height of the cone ​is equal to its radius. Find the volume of the solid in terms ​of $\pi$.
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   Volume of the solid $=\pi$ cm³ $\approx 3.14$ cm³.

   Step-by-step solution →
2. Q2
   Rachel, ​an engineering student, was asked to make a model shaped like a ​cylinder with two cones attached at its ​two ends by using ​a thin aluminium sheet. The diameter of ​the ​model is 3 cm and its length is ​12 cm. If each cone has a height of ​2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
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   Volume of air $=66$ cm³.

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3. Q3
   A gulab jamun ​contains sugar syrup up to about 30% of its volume. ​Find approximately ​how much ​syrup would be ​found in ​45 gulab jamuns, each ​shaped like a cylinder with two hemispherical ends, with length 5 cm and diameter 2.8 cm (see Fig. 12.15).

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   Volume of syrup $\approx 338$ cm${}^3$.

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4. Q4
   A pen stand made of wood is in ​the ​shape of a cuboid with four conical ​depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm ​by 3.5 cm. The radius of ​each of the ​depressions is 0.5 cm ​and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 12.16).

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   Volume of wood $\approx 523.53$ cm${}^3$ (cuboid $525$ cm${}^3$ minus four conical depressions totalling about $1.47$ cm${}^3$).

   Step-by-step solution →
5. Q5
   A vessel is in the form of an inverted cone. Its height is $8$ ​cm and the radius of its top, which is open, is $5$ cm. It ​is filled with water up to the brim. When lead shots, each ​of ​which is a sphere of radius $0.5$ cm are ​dropped ​into the vessel, one-fourth of the water flows out. ​Find the ​number of lead shots dropped in the vessel.
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   Number of lead shots $=100$.

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6. Q6
   A solid iron pole consists of a cylinder of height 220 ​cm and base diameter 24 cm, which ​is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the ​mass of the pole, given that 1 cm${}^3$ of ​iron has approximately 8 ​g ​mass. (Use $\pi =3.14$)
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   Mass of the pole $\approx 892262.4$ g $=892.26$ kg.

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7. Q7
   A ​solid ​consisting of a right circular cone of height ​120 cm and radius 60 cm standing on a hemisphere of radius 60 ​cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the ​cylinder, if the radius of the ​cylinder ​is 60 cm and its height is ​180 cm.
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   Water left $=360000\pi$ cm³ $\approx 1131428.57$ cm³ $\approx 1.131$ m³.

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8. Q8
   A spherical glass vessel has a cylindrical neck 8 cm long, ​2 cm ​in diameter; the ​diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a ​child finds its ​volume ​to be 345 cm${}^3$. Check whether she ​is correct, taking the above as the inside measurements, and $\pi =3.14$.
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   The vessel's capacity is about $346.51$ cm³, so the child is not correct ($345$ cm³ is too low).

   Step-by-step solution →