Question

The ratio of the radius of the base of a cylinder to
its height is 7 : 6. If the volume of the cylinder is
294pi cm3, then its base diameter is
(1) 1 cm (2) 14 cm
(3) 7 cm (4) 12 cm

Answer 1

Let radius and height of cylinder be 7X and 6X.




Volume of cylinder = 294π



πR²H = 294 × 22/7



πR²H = 924



22/7 × (7X)² × 6X = 924



49X² × 6X = ( 924 × 7 ) /22



294X³ = 294



X³ = 1



X = 1.





Radius of cylinder = 7X = 7 × 1 = 7 cm




Base diameter = Radius × 2 = 14 cm.


Hence,

Option ( b ) is right answer.

Answer 2

yoυr anѕwer !!

ᴠᴏʟᴜᴍᴇ ᴏғ ᴄʏʟɪɴᴅᴇʀ = 294π

ʀᴀᴛɪᴏ ᴏғ ʀᴀᴅɪᴜs ᴀɴᴅ ʜᴇɪɢʜᴛ ᴏғ ᴄʏʟɪɴᴅᴇʀ = 7:6

ʟᴇᴛ ᴛʜᴇ ᴄᴏᴍᴍᴏɴ ʀᴀᴛɪᴏ = x

sᴏ,

ʀᴀᴅɪᴜs = 7x

ʜᴇɪɢʜᴛ = 6x


$= > volume = \pi {r}^{2} h \\ \\ = > 294\pi = \frac{22}{7} \times {(7x)}^{2} \times 6x \\ \\ = > 294 \times \frac{22}{7} = \frac{22}{7} \times 49 {x}^{2} \times 6x \\ \\ = > 294 \times \frac{22}{7} \times \frac{7}{22} = 294 {x}^{3} \\ \\ = > \frac{294}{294} = {x}^{3} \\ \\ = > 1 = {x}^{3} \\ \\ => {1}^{3} = {x}^{3} \\ \\ => 1 = x$

ʜᴇɴᴄᴇ, ʀᴀᴅɪᴜs = 7x = 7 × 1 = 7ᴄᴍ

ʜᴇɪɢʜᴛ = 6x = 6 × 1 = 6ᴄᴍ

ᴅɪᴀᴍᴇᴛᴇʀ = 2ʀ = 2 × 7ᴄᴍ = 14ᴄᴍ

(2) ᴏᴘᴛɪᴏɴ ɪs ᴄᴏʀʀᴇᴄᴛ !

тнanĸѕ !!