Question

The total surface area and the curved surface area of a cone
are 704 sq. cm and 550 sq. cm respectively. Find the slant
height of the cone.
Ans: 25 cm
sne.se​

Answer 1

Answer:

Given,

Total Surface area of Cone(TSA) = 704cm²

Curved Surface Area of Cone(CSA) = 550cm²

To Find :-

Slant Height of the Cone.

Required Formula :-

Total Surface Area of the Cone(TSA) = πr(l + r) = πrl + πr²

Curved Surface Area of Cone (CSA) = πrl

Where,

π is pie

l is slant Height

r is radius.

Solution :-

Given,

πrl + πr²(TSA) = 704cm²

πrl(CSA) = 550cm²

Hence , we can substitute Value of πrl is formula of TSA .ie.

550cm² + πr² = 704cm²

πr² = 704cm² - 550cm²

$\sf\frac{22}{7}$ × r² = 154cm²

r² = 154cm² × $\sf\frac{7}{22}$

r² = 7×7cm²

r² = 49cm²

r = √49cm²

r = 7cm

Substituting value of 'r in πrl(CSA)

$\sf\frac{22}{7}$×7cm×l = 550cm²

22cm × l = 550cm²

l = $\sf\frac{550cm²}{22cm}$

l = 25cm

$\sf\therefore$ slant Height 'l' = 25cm

Answer 2

Answer:

Step-by-step explanation: