Question

1.) Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved
surface area.
2.) Find the total surface area of a cone, if its slant height is 21 m and diameter of its base
is 24 m.​

Answer 1

Step-by-step explanation:

Solutions:-

1)

Given that

Diameter of the base of a cone

(d) = 10.5 cm

We know that

Radius (r) = d/2 = 10.5/2

Radius of the cone = 5.25 cm

Slant height of the cone (l) = 10 cm

We know that

Curved Surface area of a cone

= πrl sq.units

Curved Surface Area of the given cone

= (22/7)×5.25×10 cm²

= 3.14×5.25×10 cm²

= 164.85 cm²

Curved Surface Area of the cone

= 164.85 cm²

2)

Given that

Diameter of the base of a cone

(d) = 24 m

We know that

Radius (r) = d/2 = 24/2

Radius of the cone = 12 m

Slant height of the cone (l) = 21 m

Total Surface area of a cone

= πr(l+r) sq.units

Total Surface Area of the given cone

= (22/7)×12(21+12) cm²

= 3.14×12×33 cm²

= 1243.44 cm²

Total Surface area of the cone

= 1243.44 cm²

Used formulae:-

Curved Surface area of a cone

= πrl sq.units

Total Surface area of a cone

= πr(l+r) sq.units

• r = radius
• l = slant height
• π = 22/7 = 3.14

Radius = Diameter/2

Answer 2

$\large\qquad\qquad \; \; {\pmb{\underline{\underline{\frak{ \; Question \; 1 }}}}}$

Given :

• Diameter of base = 10.5 cm
• Slant height = 10 cm

$\\ \rule{200pt}{3pt}$

To Find :

• CSA of cone = ?

$\\ \rule{200pt}{3pt}$

Solution :

~ Formula Used :

${\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\tt{ Curved \; Surface \; Area = \pi rl }}}}} \; {\color{cyan}{\bigstar}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Curved Surface Area :

${\longmapsto{\qquad{\sf{ CSA = \pi rl }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{22}{7} \times \dfrac{Diameter}{2} \times 10 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{22}{7} \times \dfrac{10.5}{2} \times 10 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{22}{7} \times \dfrac{105}{2 \times 10} \times 10 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{22}{7} \times \dfrac{105}{\cancel{20}} \times \cancel{10} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{\cancel{22}}{7} \times \dfrac{105}{\cancel2} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{11}{7} \times 105 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \dfrac{1155}{7} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ CSA = \cancel\dfrac{1155}{7} }}}} \\ \\ \ {\qquad {\therefore \; \; \; {\underline{\boxed{\purple{\sf{ CSA = 165 \; cm² }}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Therefore :

❛❛ Curved Surface Area of the given cone is 165 cm² . ❜❜

$\\ {\underline{\orange{\rule{75pt}{6pt}}}}{\underline{\green{\rule{75pt}{6pt}}}}{\underline{\red{\rule{75pt}{6pt}}}}$

$\large\qquad\qquad \; \; {\pmb{\underline{\underline{\frak{ \; Question \; 2 }}}}}$

Given :

• Slant height = 21 m
• Diameter of Base = 24 m

$\\ \rule{200pt}{3pt}$

To Find :

• TSA of cone = ?

$\\ \rule{200pt}{3pt}$

Solution :

~ Formula Used :

${\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\tt{ Total \; Surface \; Area = \pi r(l + r) }}}}} \; {\color{cyan}{\bigstar}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Total Surface Area :

${\dashrightarrow{\qquad{\sf{ TSA = \pi r(l + r) }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{22}{7} \times \dfrac{Diameter}{2} \bigg(21 + \dfrac{Diameter}{2} \bigg)}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{22}{7} \times \dfrac{24}{2} \bigg(21 + \dfrac{24}{2} \bigg)}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{22}{7} \times \cancel\dfrac{24}{2} \bigg(21 + \cancel\dfrac{24}{2} \bigg)}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{22}{7} \times 12 \bigg(21 + 12 \bigg)}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{22}{7} \times 12 \times 33}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{22}{7} \times 396}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \dfrac{8712}{7} }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = \cancel\dfrac{8712}{7} }}}} \\ \\ \ {\qquad {\therefore \; \; \; {\underline{\boxed{\orange{\sf{ TSA = 1244.57 \; m² }}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Therefore :

❛❛ Total Surface Area of the given cone is 1244.57 m² . ❜❜

$\\ {\underline{\orange{\rule{75pt}{6pt}}}}{\underline{\green{\rule{75pt}{6pt}}}}{\underline{\red{\rule{75pt}{6pt}}}}$