# from a solid cylinder whose height is 12 cm and diameter is 10 cm, a conical cavity of same height and same diameter is hollowed out. find the volume and total surface area of the remaining solid.

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## From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.

Click here👆to get an answer to your question ✍️ From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.

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## From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.

Medium Open in App Solution Verified by Toppr

Volume of remaining solid = volume of cylinder - volume of cone.

r=5 cm (given) h=12 cm

Volume of cylinder = πr

2 h =3.14×5 2 ×12 =942cm 2 Volume of cone = 3 1 πr 2 h= 3 1 ×3.14×5 2 ×12 =314cm 3

Remaining volume = 942-314

=628cm 3

Total surface of remaining solid = conical sutface area of cone + Area of circle + Cylindrical area of cylinder.

Conical sutface area of cone =πr

r 2 +h 2 =204.203 cm 2

Conical of cirle = πr

2 =78.54cm 2

Cylindrical area of cylinder = 2πrh

=376.8cm 2

Total surface area 659.543cm

2

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## From a solid cylinder of height 12 cm and base diameter 10 cm, a conical cavity with the same height and diameter is carved out. Find the volume of the remaining solid.

From a solid cylinder of height 12 cm and base diameter 10 cm, a conical cavity with the same height and diameter is carved out. Find the volume of the remaining solid.

Byju's Answer Standard X Mathematics

Volume of a Right Circular Cone

From a solid ... Question

From a solid cylinder of height

12 cm and base diameter 10 cm

, a conical cavity with the same height and diameter is carved out. Find the volume of the remaining solid.

Open in App Solution

**Step 1: Given information**

The height of the cylinder and cone

h is 1 12 cm .

The radius of the cylinder and cone

r is 102=5 cm

**Step 2: Determine the volume of the cylinder**

V1

**and cone**

V2

**.**

The volume of the cylinder

V is calculated by π π V=πr2h π π V1=π×52×12=300π cm3

The volume of the cone

V' is calculated by π π V'=13πr2h . π π

V2=13π×52×12=100π cm3

**Step 3: Determine the volume of the remaining solid**

ππ π ππ π

Volume of the remaining solid = V1 -V2=300π-100π=200π=200×227=628.57 cm3

Hence, the volume of the remaining solid is

628.57 cm3 . Suggest Corrections 5

SIMILAR QUESTIONS

**Q.**From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. [CBSE 2014]

**Q.**From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use

π = 3.14)

**Q.**From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.

**Q.**From a solid cylinder of height

7

cm and base diameter

12

cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid.

[ U s e π = 22 7 ] .

**Q.**

from a solid cylinder whose height is 2.4sm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out. Find the volume of the remaining solid to the nearest cm cube

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Standard X Mathematics

## From a solid cylinder whose height is 12 cm and diameter 10 cm , a conical cavity with the same base and height is taken out . Find the total surface area of the ramaining solid .

From a solid cylinder whose height is 12 cm and diameter 10 cm , a conical cavity with the same base and height is taken out . Find the total surface area of

From a solid cylinder whose height is 12 cm and diameter 10 cm , a conical cavity with the same base and height is taken out . Find the total surface area of the ramaining solid .

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OSWAL PUBLICATION-DIKSHA QUESTIONS -UNIT -VI: AREA RELATED TO CIRCLE (SURFACE AREAS AND VOLUMES) (SHORT ANSWER TYPE QUESTIONS )

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