Question

curved surface area of a cone is 308 cm^2 and its slant height is 14 cm. Find the base area and its volume​

Answer 1

• Base area of cone is 154 cm².
• Volume of cone is 622.16

Step-by-step explanation:

Given:-

• Curved surface area of cone is 308 cm².
• Slant height of cone is 14 cm.

To find:-

• Base area of cone.
• Volume of cone.

Solution:-

Here,

• First we will find base radius of cone by using curved surface area of cone for finding base area.

• Then we will find height of cone using base radius and Slant height of cone for volume of cone.

Curved surface area of cone = πrl

Where,

• r is radius and l is slant height of cone.

Put Curved surface area and l in formula :

$\longrightarrow$ 308 = 22/7 × r × 14

$\longrightarrow$ 308 = 308/7 × r

$\longrightarrow$ 308 = 44 × r

$\longrightarrow$ r = 308/44

$\longrightarrow$ r = 7

Base radius of cone is 7 cm.

Base area = πr² [r is base radius]

Put r in formula :

$\longrightarrow$ 22/7 × (7)²

$\longrightarrow$ 22/7 × 49

$\longrightarrow$ 1078/7

$\longrightarrow$ 154

Base area of cone is 154 cm².

l = √r² + h²

[Where, l is slant height, r is radius and h is height of cone]

By this,

h = √l² - r²

$\sf \rightarrow h = \sqrt{(14)^{2} - (7)^{2}}$

$\sf \rightarrow h = \sqrt{196 - 49}$

$\sf \rightarrow h = \sqrt{147}$

$\sf \rightarrow \bold{h = 12.12}$

Height of cone is 12.12 cm.

Volume of cone = 1/3 πr²h

Put h and r in formula:

$\longrightarrow$ 1/3 × 22/7 × (7)² × 12.12

$\longrightarrow$ 22/21 × 49 × 12.12

$\longrightarrow$ 13065.36/21

$\longrightarrow$ 622.16

Volume of cone is 622.16 cm³.

Answer 2

Answer:

Base area = 154 cm²

Volume = 622.16 cm³

Step-by-step explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• CSA of cone = 308 cm²
• Slant height (l) = 14 cm

$\underline{\bigstar\:\textsf{To\:find:}}$

• Base area = ?
• Volume = ?

$\underline{\bigstar\:\textsf{Solution:}}$

We know, $\sf{\underline{curved\:surface\:area\:of\:cone\:=\:\pi\:rl}}$

Let's find radius first !

$\longrightarrow\:\sf{308\:=\:\dfrac{22}{7}\:\times\:r\:\times\:14}$

$\longrightarrow$ 308 = 22 × 2 × r

$\longrightarrow\:\sf{\dfrac{308}{22\:\times\:2}}$

$\therefore$ Radius = 7 cm.

Now, the base of a cone is a circle, so the base area = $\sf{\pi}$r²

$\longrightarrow\:\sf{Base\:area\:=\:\dfrac{22}{7}\:\times\:(7)^2}$

$\longrightarrow\:\sf{Base\:area\:=\:\dfrac{22}{7}\:\times\:49}$

$\longrightarrow$ Base area = 22 × 7

$\therefore$ Base area of cone if 154 cm²

Now, we know that volume of cone = $\sf{\dfrac{1}{3}\pi\:r^2h}$

Here, we don't know the height but we know that $\sf{l^2\:=\:r^2+h^2}$

So, h = $\:\sf{\sqrt{l^2-r^2}}$

$\longrightarrow\:\sf{h\:=\:\sqrt{(14)^2-(7)^2}}$

$\longrightarrow\:\sf{h\:=\:\sqrt{196\:-\:49}}$

$\longrightarrow\:\sf{h\:=\:\sqrt{147}}$

$\therefore$ Height of cone = 12.12 cm.

Now, we will find the volume.

$\longrightarrow\:\sf{V\:=\:\dfrac{1}{3}\:\times\:\dfrac{22}{7}\:\times\:(7)^2\:\times\:12.12}$

$\longrightarrow\:\sf{V\:=\:\dfrac{22}{21}\:\times\:49\:\times\:12.12}$

$\longrightarrow$ Volume of cone is 622.16 cm³.