the height of a solid cylinder is 10 cm and the diameter is 8 cm. two equal conical holes have been made from both ends. if the diameter of the hole is 6 cm and the height is 4 cm, then the volume of the remaining solid is

get the height of a solid cylinder is 10 cm and the diameter is 8 cm. two equal conical holes have been made from both ends. if the diameter of the hole is 6 cm and the height is 4 cm, then the volume of the remaining solid is from screen.

Height of a solid cylinder is 10cm and diameter 8cm . Two equal conical holes have been made from its both ends. If the diameter of the holes is 6cm and height 4cm , find (i) volume of the cylinder (ii) volume of one conical hole, (iii) volume of the remaining solid.

Click here👆to get an answer to your question ✍️ Height of a solid cylinder is 10cm and diameter 8cm . Two equal conical holes have been made from its both ends. If the diameter of the holes is 6cm and height 4cm , find (i) volume of the cylinder (ii) volume of one conical hole, (iii) volume of the remaining solid.

Question

Height of a solid cylinder is 10cm and diameter 8cm. Two equal conical holes have been made from its both ends. If the diameter of the holes is 6cm and height 4cm, find (i) volume of the cylinder  (ii) volume of one conical hole, (iii) volume of the remaining solid.

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Updated on : 2022-09-05

Given,

Solution Verified by Toppr

Height of the cylinder, H=10 cm

Diameter of Base of the cylinder, d=8 cm

Hence, the radius of the cylinder, R=

2 d ​ =4 cm

Two conical holes are cutoff from the cylinder.

Height of the cone h=4 cm

Diameter of the cone D=6 cm

Hence, Radius of the cone, r=

2 D ​ =3 cm Now,

Volume of the cylinder  V=πR

2 H V=π×4 2 ×10 cm 3 V=π×16×10 cm 3 V=160π cm 3

Hence, volume of cylinder is 160π cm

3

Volume of the cone v=

3 1 ​ πr 2 h v= 3 1 ​ ×π×3 2 ×4 cm 3 v=π×3×4 cm 3 v=12π cm 3

Hence, volume of one conical hole is 12π cm

3

The volume of the remaining solid = Volume of the cylinder - 2 (Volume of the cone )

=(160−2×12)π cm 3 =(160−24)π cm 3 =136π cm 3

Hence, volume of remaining solid is 136π cm

3

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Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical hole have been made from its both ends. If the diameter oaf the holes is 6 cm and height 4 cm, find i volume of the cylinder, ii volume of one conical hole, iii volume of the remaining solid.

Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical hole have been made from its both ends. If the diameter oaf the holes is 6 cm and height 4 cm, find i volume of the cylinder, ii volume of one conical hole, iii volume of the remaining solid.

Byju's Answer Standard X Mathematics

Volume of Combined Solids

Height of a s... Question

Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical hole have been made from its both ends. If the diameter oaf the holes is 6 cm and height 4 cm, find (i) volume of the cylinder, (ii) volume of one conical hole, (iii) volume of the remaining solid.

Open in App Solution Height = 10 cm. Radius

(i) Volume of cylinder

= π π 160πcm3

(ii) Volume of conical hole diameter of

cone = 6 cm.

(iii) Volume of remaining solid

= π π 136πcm3 Suggest Corrections 1

SIMILAR QUESTIONS

Q. Height of a solid cylinder is

10 cm and diameter 8

cm. Two equal conical holes have been made from both the ends of cylinder. If the diameter of the hole is

6 m and height 4

cm. The volume of the remaining portion is

Q. From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid. [CBSE 2011]Q. From a solid cylinder of height

14 c m and base diameter 7 c m

, two equal conical holes each of radius

2.1 c m and height 4 c m

are hollowed out. Find the volume of the remaining solid.

Q. The height of a solid cylinder is

15 c m

, and the diameter of its base is

7 c m

. Two equal conical holes each of radius

3 c m , and height 4 c m

are cut off. Find the volume of the remaining solid.

Q.

From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.

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Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical holes have been made from its both ends of diameter of the hole is 6 cm and height is 4 cm. Find the volume of the cylinder, the volume of one conical hole and the volume of remaining solid.

Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical holes have been made from its both ends of diameter of the hole is 6 cm and height is 4 cm. Find the volume of the cylinder, the volume of one conical hole and the volume of rem...

Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical holes have been made from its both ends of diameter of the hole is 6 cm and height is 4 cm. Find the volume of the cylinder, the volume of one conical hole and the volume of remaining solid.

Last updated date: 15th Mar 2023

• Total views: 289.5k • Views today: 3.69k Answer Verified 289.5k+ views 1 likes

Hint: To solve the question, we have to apply the formula for volume of cylinder and volume of cone to calculate the answer. To answer the last question, we have to analyse that the volume of the remaining solid is equal to difference of the volume of the solid cylinder and the volume of the two conical holes.

Complete step-by-step answer:

The given height of a solid cylinder is equal to 10 cm.

The given diameter of a solid cylinder is equal to 8 cm.

We know the formula for the volume of the cylinder is given by

π r 2 h πr2h

Where h, r are the height and radius of the cylinder respectively.

We know diameter = 2(radius). Thus, we get

8=2r r= 8 2 =4cm 8=2rr=82=4cm

By substituting the given values in the above formula, we get

π (4) 2 10 =π×16×10 =160π

π(4)210=π×16×10=160π

Thus, the volume of the solid cylinder is equal to

160π 160π cubic cm.

The given height of a conical hole is equal to 4 cm.

The given diameter of a conical hole is equal to 6 cm.

We know the formula for the volume of the cone is given by

1 3 π r 2 h 13πr2h

Where h, r are the height and radius of the cone respectively.

We know diameter = 2(radius). Thus, we get

6=2r r= 6 2 =3cm 6=2rr=62=3cm

By substituting the given values in the above formula, we get

1 3 π (3) 2 4 =π(3)4 =12π 13π(3)24=π(3)4=12π

Thus, the volume of one conical hole is equal to

12π 12π cubic cm.

The volume of the remaining solid = The volume of the solid cylinder –the volume of the conical holes

Since, there are two conical holes, we get

The volume of the remaining solid = The volume of the solid cylinder – 2(the volume of one conical hole)

By substituting the given values in the above formula, we get

=160π−2(12π) =160π−24π =136π

=160π−2(12π)=160π−24π=136π

Thus, the volume of the remaining solid is equal to

136π 136π

Note: The possibility of mistake can be, not applying the formula for volume of cylinder and volume of cone to calculate the answer. The other possibility of mistake can be, not analysing that the volume of the remaining solid is equal to difference of the volume of the solid cylinder and the volume of the two conical holes.

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