Q1) Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Q2) Find the total surface area of a cone, if its slant height is 21 m and diameter of its base in 24m.
Q3) Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.
Answers & Comments
Answer:
Q1) Curved Surface Area = 165 cm²
Q2) Total surface area = 1244.57 m²
Q3) Radius = 7 cm and Total surface area = 462 cm²
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-1}}[/tex]
Given that, Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm.
So, we have
Slant height of a cone l = 10 cm
Radius of cone, r = 5.25 cm
Now, Consider
[tex] \sf \: Curved\:surface\:area\:of\:cone = \pi \: r \: l \\ [/tex]
[tex] \sf \:Curved\:surface\:area\:of\:cone = \dfrac{22}{7} \times 5.25 \times 10\\ [/tex]
[tex] \sf \:Curved\:surface\:area\:of\:cone = 22 \times 0.75 \times 10\\ [/tex]
[tex] \implies\bf\: Curved\:surface\:area\:of\:cone = 165 \: {cm}^{2} \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex]\large\underline{\sf{Solution-2}}[/tex]
Given that, slant height of cone is 21 m and diameter of its base is 24 m.
So, we have
Slant height of a cone l = 21 m
Radius of cone, r = 12 m
Now, Consider
[tex] \sf \:Total\:surface\:area\:of\:cone = \pi \: r \:( l + r)\\ [/tex]
[tex] \sf \: Total\:surface\:area\:of\:cone = \dfrac{22}{7} \times 12 \times (12 + 21) \\ [/tex]
[tex] \sf \: Total\:surface\:area\:of\:cone = \dfrac{22}{7} \times 12 \times 33 \\ [/tex]
[tex]\implies\bf\: Total\:surface\:area\:of\:cone = 1244.57 \: {m}^{2} \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex]\large\underline{\sf{Solution-3}}[/tex]
Given that,
Curved surface area of a cone = 308 cm²
Slant height of a cone, l = 14 cm
Let assume that radius of a cone be r cm.
As we have,
[tex] \sf \: Curved\:surface\:area\:of\:cone = 308 \\ [/tex]
[tex] \sf \: \pi \: r \: l = 308 \\ [/tex]
[tex] \sf \: \dfrac{22}{7} \times r \times 14= 308 \\ [/tex]
[tex] \sf \: 22 \times r \times 2 = 308 \\ [/tex]
[tex] \sf \: 22 \times r = 154 \\ [/tex]
[tex]\implies\sf\:r = 7 \: cm \\ [/tex]
Now,
[tex] \sf \: Total\:surface\:area\:of\:cone = \pi \: r \: (l + r) \\ [/tex]
On substituting the values, we get
[tex] \sf \: Total\:surface\:area\:of\:cone = \dfrac{22}{7} \times 7 \times (14 + 7) \\ [/tex]
[tex] \sf \: Total\:surface\:area\:of\:cone = 22 \times 21 \\ [/tex]
[tex]\implies\bf\: Total\:surface\:area\:of\:cone = 462 \: {cm}^{2} \\ [/tex]