VOLUME & SURFACE AREA OF CONE BY MAYANK AGNIHOTRI
O CONE Cone is a solid or hollow body with a round base and pointed top. It is also formed by the rotation of a right angled triangle along any of its sides. . Volume=-x Base area x Height =7Tr2h * Slant height ()V+hz . Curved surface area 1 MTVr2 + h2 . Total surface area = curved surface area + Area of base = rl tTr2- (r + 1) Where, r Radius of base h Height and l Slant height heiyht
FRUSTUM OF CONE If a cone is cut from the top to divide the cone into two parts upper part and lower part, then the lower part is called frustum of cone. Volume hR2 + rR) Slant height (l) -V(R - r)2 + h2 . curved surface area or lateral surface area- (R + r)! Total surface area = Area of top surface + bottom surface + Curved surface area heisht Where, r Radius of top, R- Radius of base (bottom), h- Height and l-Slant height
Questions Ques 1. What is the volume of a cone having a base of radius 10 cm and height 21 cm? Sol. Volume of cone =rr2h 3 = 102 21 = 2200 cm3 Ans Ques 2. The diameter of base of a right circular cone is 6 cm and slant height is 14 cm, then what is its curved surface area? So Given, Diameter of a right circular cone 6 cm Radius of a right circular cone 3 cm slant height of a right circular cone ()14 cm =-= .: curved surface area of a cone-tri = 22 3 14 = 132 cm2
Ques 3. The volume of frustum of a cone left after cutting it by a plane parallel to its base at half the height is how many times of the volume of cone. (1) (2) (3) (4) Sol. Volume of frustum of cone = 3 hfof+RF+TjRf) Here, Rf= r , Tj = 5 & hf = 2 (92+r2+ 1 Volume of frustum of cone =- 1 h [r2 3 2L4 7 Volume of cone =7TY2h Ans =
Ques 4. Slant height of a cone is 10 cm and height Is 8 cm. Find the Curved surface area of cone. Sol. slant height (l) = Vr4hz radius (102-87-100-64 36 6 cm curved surface area of cone-Tri = 22 6 10 = 188.6 cm2 Ans I10 cm &h 8 cm given ]
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