Question

From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same the height and same radius is cut out. Find the total surface area of the remaining solid.

Answer 1

Step 1: The first step is to find the dimensions of the cone.

We are given the dimensions of the cylinder. A cone with the same height and radius as the cylinder has been carved out, implying that the cone's radius and height are identical to those of the cylinder.

Radius of the cone $\left(r\right)=0.7cm$
Height of the cone $\left(h\right)=2.4cm$
Slant height $\left(l\right)$ can be found out by:
$l^2=r^2+h^2={0.7}^2+{2.4}^2=6.25$
$l=\sqrt{6.25}=2.5cm$

Step 2: The second step is to calculate the curved surface area of the cylinder.

CSA of cylinder = $2\pi rh$
= $2\times \left(\frac{22}{7}\right)\times 0.7\times 2.4$
= $10.56c{m}^2$

Step 3: The third step is to calculate the curved surface area of the cone.

CSA of cone = $\pi rl$
= $\left(\frac{22}{7}\right)\times 0.7\times 2.5$
= $5.5c{m}^2$

Step 4: The fourth step is to calculate the base area of the cylinder.

Base area of cylinder = $\pi r^2$
= $\left(\frac{22}{7}\right)\times {0.7}^2$
= $1.54c{m}^2$

Step 5: The final step is to calculate the surface area of the resultant solid.

This can be found out by:
Surface area of solid = CSA of Cylinder + CSA of Cone + base area of cylinder
= $10.56c{m}^2+5.5c{m}^2+1.54c{m}^2$
= $17.6c{m}^2$