Question

The radius and slant height of a cone are in the ratio
8:17. If its curved surface area is 5441 cm”, then find
3
its volume.
(a) 2560 cm3
(c) 26701 cm
(b) 27607 cm
(d) 25601 cm
3​

Answer 1

Answer:

Let's take r=8xr=8x , and l=17xl=17x .

The CSA is given as 54\pi cm^{2}54πcm

2

.

CSA=\pi rlCSA=πrl

54\pi=\pi rl54π=πrl

We can cancel the \piπ :

54=rl54=rl

54=8x \times 17x54=8x×17x

54=136x^{2}54=136x

2

x^{2}=\frac{54}{136}x

2

=

136

54

x=\sqrt{\frac{27}{68}}x=

68

27

Radius:

r=8xr=8x

r=8 \times \sqrt{\frac{27}{68}}r=8×

68

27

r \approx 5.041r≈5.041

Slant height:

l=17xl=17x

l=17 \times \sqrt{\frac{27}{68}}l=17×

68

27

l \approx 10.712l≈10.712

We must also find the height to find the volume.

h^{2}=l^{2}-r^{2}h

2

=l

2

−r

2

h=\sqrt{l^{2}-r^{2}}h=

l

2

−r

2

h=\sqrt{10.712^{2}-5.041^{2}}h=

10.712

2

−5.041

2

h \approx 9.451h≈9.451

Now, we need to find the volume, which is \frac{1}{3}\pi r^{2} h

3

1

πr

2

h

V=\frac{1}{3}\pi r^{2} hV=

3

1

πr

2

h

r \approx 5.041r≈5.041 and h \approx 9.451h≈9.451

V=\frac{1}{3}\pi \times 5.041^{2} \times 9.451V=

3

1

π×5.041

2

×9.451

V=\pi \times 25.411 \times 3.15V=π×25.411×3.15

V=251.467 cm^{3}V=251.467cm

3

Therefore, the volume is 251.467 cm^{3}cm

3

.

Answer 2

Answer:

let the radius and the slant height of the cone be 8x and 17 x respectively

height of the cone = l =√r²+h²= √17 x²-8x² = 15 x

the csa of the cone = πrl sq. units

=22/7 *8x*17 x =544π = x²= 4 and x =2

radius of a cone = 30 cm

volume of a cone = 1/3 πr²h =1/3 π(16)²*30 = 2560 πcm³

therefore the correct option is a

hope it will help!!