Question

Find the total surface area of a right circular cone, if the height of the cone is 10cm and the circumference of the base is 88 cm​

Answer 1

Answer:

1372.8 cm² is the required answer

Step-by-step explanation:

According to the Question

It is given that ,

• Height of cone ,h = 10cm
• circumference of the base , = 88cm

we need to calculate the total surface area of the right circular cone .

Calculating the radius of the cone.

➻ Circumference = 2πr

➻ 88 = 2×22/7 × r

➻ 88×7/2×22 = r

➻ 4×7/2 = r

➻ 2×7 = r

➻ 14 = r

➻ r = 14cm.

Calculating the slant height of the cone .

➻ l = √h²+r²

➻ l = √10²+14²

➻ l = √100+196

➻ l = √296

➻ l = 17.20 cm

Now,

Calculating the total surface area of the cone.

• TSA of cone = πr(l+r)

substitute the value we get

➻ TSA of cone = 22/7 × 14 (17.20+14)

➻ TSA of cone = 22×2 (31.20)

➻ TSA of cone = 44× 31.20

➻ TSA of cone = 1372.8cm²

• Hence, the total surface area of the right circular cone is 1372.8 cm²

Answer 2

Given :-

Height = 10 cm

Circumference = 88 cm

To Find :-

TSA

Solution :-

We know that

${\boxed{\frak{\red{\underline{Circumference= 2\pi r}}}}}$

Let the radius be r

$\sf :\implies 88=2\pi r$

$\sf :\implies 88 = 2\times\dfrac{22}{7}\times r$

$\sf :\implies 88=\dfrac{44}{7}\times r$

$\sf :\implies \dfrac{88\times7}{44}=r$

$\sf :\implies 2\times7=r$

$\sf :\implies 14=r$

${\boxed{\frak{\pink{\underline{l^2 = h^2+r^2}}}}}$

$\sf :\implies l^2 = (14)^2+(10)^2$

$\sf :\implies l^2 = 196+100$

$\sf :\implies l^2= 296$

$\sf :\implies l=\sqrt{296}$

$\sf :\implies l = 17.2$

${\boxed{\frak{\red{\underline{TSA = \pi r(r+l)}}}}}$

$\sf :\implies TSA=\dfrac{22}{7}\times 14(17.2 + 14)$

$\sf :\implies TSA=\dfrac{22}{7}\times 14\times 31.2$

$\sf :\implies TSA = 22\times2\times31.2$

$\sf :\implies TSA = 1372.8$

$\bf{\underline{Hence, \;TSA \;of \;cone\; is\; 1372.8 \;cm}}$