Question

the curved surface area of a cone exceeds the base area by 88 CM square its slant height exceeds the base radius by 4 cm find the base radius

Answer 1

curved surface area
$\pi(r)l$
area of base
$\pi {r}^{2} \\ \pi(r)l = 88 + \pi {r}^{2}$
slant height =4 + radius
$\frac{22}{7} \times r \times (4 + r) = 88 + \frac{22}{7} \times {r}^{2} \\ 4r + {r}^{2} = 88 + {r}^{2} \\ 4r = 88 + {r}^{2} - {r}^{2} \\ 4r = 88 \\ r = 22cm$
Base radius is 22cm

Answer 2

Answer:

The base radius is 22cm.

Step-by-step explanation:

Given : The curved surface area of a cone exceeds the base area by 88 CM square its slant height exceeds the base radius by 4 cm

To find : The base radius ?

Solution :

The curved surface area is $CSA=\pi(r)l$

The area of base  $A=\pi(r)^2$

According to question,

The curved surface area of a cone exceeds the base area by 88 CM square

$\pi(r)l = 88 + \pi {r}^{2}$

also, slant height exceeds the base radius by 4 cm

$l=4+r$

Substitute,

$\frac{22}{7}  \times r \times (4 + r) = 88 +  \frac{22}{7}  \times  {r}^{2}$

$4r + {r}^{2}  = 88 + {r}^{2}$

$4r = 88 +{r}^{2}-{r}^{2}$

$4r = 88$

$r = 22cm$

Therefore, The base radius is 22cm.