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]

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]

Solution−1

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]\begin{gathered} \sf \: Curved\:surface\:area\:of\:cone = \pi \: r \: l \\ \end{gathered} [/tex]

[tex]\begin{gathered} \sf \:Curved\:surface\:area\:of\:cone = \dfrac{22}{7} \times 5.25 \times 10\\ \end{gathered}[/tex]

[tex]\begin{gathered} \sf \:Curved\:surface\:area\:of\:cone = 22 \times 0.75 \times 10\\ \end{gathered} [/tex]

[tex]\begin{gathered} \implies\bf\: Curved\:surface\:area\:of\:cone = 165 \: {cm}^{2} \\ \end{gathered} [/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]\begin{gathered} \sf \:Total\:surface\:area\:of\:cone = \pi \: r \:( l + r)\\ \end{gathered} [/tex]

[tex]\begin{gathered} \sf \: Total\:surface\:area\:of\:cone = \dfrac{22}{7} \times 12 \times (12 + 21) \\ \end{gathered} [/tex]

[tex]\begin{gathered} \sf \: Total\:surface\:area\:of\:cone = \dfrac{22}{7} \times 12 \times 33 \\ \end{gathered} [/tex]

[tex]\begin{gathered}\implies\bf\: Total\:surface\:area\:of\:cone = 1244.57 \: {m}^{2} \\ \end{gathered} [/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]\begin{gathered} \sf \: Curved\:surface\:area\:of\:cone = 308 \\ \end{gathered} [/tex]

[tex]\begin{gathered} \sf \: \pi \: r \: l = 308 \\ \end{gathered}

[/tex]

[tex]\begin{gathered} \sf \: \dfrac{22}{7} \times r \times 14= 308 \\ \end{ggathered}[/tex]

[tex]\begin{gathered} \sf \: 22 \times r \times 2 = 308 \\ \end{gathered}

[/tex]

[tex]\begin{gathered} \sf \: 22 \times r = 154 \\ \end{gathered} [/tex]

[tex]\begin{gathered}\implies\sf\:r = 7 \: cm \\ \end{gathered} [/tex]

Now,

[tex]\begin{gathered} \sf \: Total\:surface\:area\:of\:cone = \pi \: r \: (l + r) \\ \end{gathered} [/tex]

On substituting the values, we get

[tex]\begin{gathered} \sf \: Total\:surface\:area\:of\:cone = \dfrac{22}{7} \times 7 \times (14 + 7) \\ \end{gathered}

[/tex]

[tex]\begin{gathered} \sf \: Total\:surface\:area\:of\:cone = 22 \times 21 \\ \end{gathered} [/tex]

[tex]\begin{gathered}\implies\bf\: Total\:surface\:area\:of\:cone = 462 \: {cm}^{2} \\ \end{gathered} [/tex]