Question

From a solid cylinder whose height is 2.4cm and diameter 1.4 cm, a conical cavity of the same diameter and same height is hollowed out . Find the volume of the remaining solid . *
1.964cm³
2.912cm³
3.464cm³
2.464cm³

Answer 1

Answer :

• Volume of remaining solid is 2.464cm³

Step-by-step explanation:

$\dag\:\:\underline{\sf Required\: Solution :}$

First we will write the known values which are provided in the question :

• Height of cylinder (h) = 2.4 cm
• Diameter of cylinder (d) = 1.4 cm
• Height of cone (h) = 2.4 cm
• Diameter of cone (d) = 1.4 cm

If diameter of the cylinder is equal to the diameter of the cone then the radius of cylinder will also equal to the radius of cone.

• Radius of cylinder = Radius of cone

Now, let's find the radius of the cylinder and cone :

$:\implies \sf Radius = \dfrac{Diameter}{2}$

$:\implies \sf Radius = \dfrac{1.4}{2}$

$:\implies \underline{ \boxed{ \sf Radius = 0.7 \: cm}}$

Hence,the radius of cylinder and cone is 0.7 cm.

Now, as per question we are asked to find the volume of the remaining solid. To calculate volume of the remaining solid we will use the given below formula :

$:\implies \tt Volume \: of \: remaining \: solid = Volume \: of \: cylinder - Volume \: of \: cone$

• Volume of cylinder = πr²h
• Volume of cone = ⅓πr²h

Now, just simply plug in the known values in above formula :

$:\implies \tt Volume \: of \: remaining \: solid = \pi {r}^{2}h - \dfrac{1}{3} \pi {r}^{2}h$

$:\implies \tt Volume \: of \: remaining \: solid = \dfrac{22}{7} \times {(0.7)}^{2} \times 2.4 - \dfrac{1}{3} \times \dfrac{22}{7} \times {(0.7)}^{2} \times 2.4$

$:\implies \tt Volume \: of \: remaining \: solid = \dfrac{22}{7} \times 0.49 \times 2.4 - \dfrac{1}{3} \times \dfrac{22}{7} \times 0.49 \times 2.4$

$:\implies \tt Volume \: of \: remaining \: solid = \dfrac{22}{7} \times 1.176 - \dfrac{1}{3} \times \dfrac{22}{7} \times 1.176$

$:\implies \tt Volume \: of \: remaining \: solid = 3.696- \dfrac{1}{3} \times 3.696$

$:\implies \tt Volume \: of \: remaining \: solid = 3.696- \dfrac{3.696}{3}$

$:\implies \tt Volume \: of \: remaining \: solid = 3.696- 1.232$

$:\implies \underline{ \boxed{\tt Volume \: of \: remaining \: solid = 2.464 \: {cm}^{3}}}$

Hence,the Volume of remaining solid is (D) 2.464 cm³.

Answer 2

Answer:

The volume of remaining solid will be 2.46 cm³.

Step-by-step explanation:

Given:-

• Height of cylinder (h) = 2.4 cm
• Diameter of cylinder (2r) = 1.4 cm

To find:-

• Volume of the remaining solid.

Solution:-

According to the question,

• Height of the cylinder = Height of the conical cavity = 2.4 cm

• Diameter of the cylinder = Diameter of the conical cavity = 1.4 cm

We know,

• ${\boxed{\large{\sf{Radius (r)=\dfrac{Diameter}{2}}}}}$

Then,

Radius of cylinder and conical cavity = 1.4/2 = 0.7 cm

We know,

✯${\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}$

✯ ${\boxed{\sf{Volume\: of\:cone=\dfrac{1}{3}\pi\:r^2h}}}$

Volume of the remaining solid will be,

= Volume of cylindrical - Volume of cone

= πr²h - ⅓πr²h

= πr²h (1-⅓)

• [ Put values]

= 22/7 × 0.7×0.7×2.4×2/3 cm³

= 2.46 cm³

___________________