The document Facts That Matter- Surface Areas and Volumes Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.

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**Facts that Matter**

An object having definite shape and size is called a solid.

Solids like a book, a tile, a match box, an almirah, a room, etc. are called cuboids.

Solids like dice, ice-cubes, sugar-cubes, etc. are called cubes.

Solids like jars, circular pillars, circular pipes, circular pencils, gas jars, road rollers, etc. are called cylinders.

Solids like conical tents, ice-cream cones, funnels, etc. are called cones.

Solids like cricket balls, footballs etc., are called spheres.

When a cone is cut by a plane parallel to the base of the cone then the portion between the plane and the base is called the frustum of the cone

**NOTE: ****I.** Solids like rubber tubes, iron pipes etc., are called hollow cylinders.**II. **A plane through the centre of a sphere cuts it into two equal parts. Each part is called a hemisphere.

We also know that:

I.** **For a cuboid of length = l, breadth = b and height = h, we have:

(i) Volume = (l Ã— b Ã— h) cu. units.

(ii) Lateral surface area = [2 (l + b) Ã— h] sq. units.

(iii) Total surface area = [2 (lb + bh + hl] sq. units.

II.** **For a cylinder of base radius = r and height (or length) = h, we have:

(i) Volume = Ï€r^{2}h cu. units.

(ii) Curved surface area = 2Ï€rh sq. units.

(iii) Total surface area = 2Ï€r (h + r) sq. units.

III.** **For a hollow cylinder having external radius = R, internal radius = r and height = h, we have:

(i) Volume

= [External volume] âˆ’ [Internal volume]

=(Ï€R^{2}h âˆ’ Ï€r^{2}h) cu. units = Ï€(R^{2} âˆ’ r^{2}) cu. units.

(ii) Curved surface area

= [External S.A.] + [Internal S.A.]

=[2Ï€Rh + 2Ï€rh] sq. units = 2Ï€h (R + r) sq. units

(iii) Total surface area

= (curved S.A.) + (area of the base-ring)

= [(2Ï€Rh + 2Ï€rh) + 2 (Ï€R^{2} âˆ’ Ï€r^{2})] sq. units

= [(2Ï€h (R + r) + 2Ï€ (R^{2} âˆ’ r^{2})] sq. units

IV. For a cone of base radius = r, height = h and slant height l =we have:

(i) Volume = 1/3 Ï€r^{2}h cu. units.

(ii) Curved surface area = Ï€rl sq. units.

(iii) Total surface area = [Curved surface area] + [Area of base]

= [Ï€rl + Ï€r^{2}] sq. units = Ï€r (l + r) sq. units.

V. For a sphere of radius r, we have:

(i) Volume = 4/3 Ï€r^{3} cu. units.

VI.** **For a hemisphere of radius r, we have:

(i) Volume = 2/3 Ï€r^{3} cu. units.

(ii) Surface area = 2Ï€r^{2} sq. units.

(iii) Total surface area = 3Ï€r^{2} sq. units.

VII. For a frustum of a cone of base radius = R, top radius = r, height = h and slant height = l, we have:

(i) Volume = Ï€h/3 [R^{2} + r^{2} + Rr] cu. units.

(ii) Lateral surface area

= Ï€l (R + r) sq. units, where l^{2} = h^{2} + (R âˆ’ r)^{2}

(iii) Total surface area

= [(area of base) + (area of top) + (lateral surface area)]

= [Ï€R^{2} + Ï€r^{2} + Ï€l (R + r)] sq. units.

= Ï€ [R^{2} + r^{2} + l (R + r)] sq. units.

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