The radius and height of a right circular cone are in the ratio 3:4. Then the ratio of total surface area of the cone to its curved surface area is

$2 : 3$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$3 : 5$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$7 : 9$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$8 : 5$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$8 : 5$

Let 'r' be the radius of the cone and 'h' be its height.
Given, r : h = 3 : 4.
Let $r = 3 x$ and $h = 4 x$ .
We know, slant height is given by,
$l = \sqrt{h^{2} + r^{2}}$
$⟹ l = \sqrt{(3 x)^{2} + (4 x)^{2}}$
$⟹ l = 5 x$

Required ratio $= \frac{TSA}{CSA} = \frac{π r (r + l)}{π r l} = \frac{(r + l)}{l} = \frac{(3 x + 5 x)}{5 x} = \frac{8 x}{5 x}$

$∴ Required ratio = 8 : 5$

Suggest Corrections

Similar questions

The radius and height of a right circular cone are in the ratio $4 : 3$ and its volume is $2156 c m^{3}$ . Find the curved surface area of the cone.

The radius and height of a right circular cone are in the ratio 3:4. Then the ratio of total surface area of the cone to its curved surface area is

The ratio of the radius to the height of a right cone is 3:4. Then the ratio of total surface area to curved surface of the cone is____.

3 : 5

60 π s q . c m

The radius and height of a right cone are in the ratio 3:4. The ratio of the total surface area to the curved surface of the cone is:

Join BYJU'S Learning Program