Question

The volume of a cylinder is half of its total surface area. If the radius of its base is 7 cm, find the volume ​

Answer 1

Answer:

22cucm

Step-by-step explanation:

firstly we found total surface area of cylinder

total surface area=2πr

=2×22/7×7

=44 (7 and 7 get cancelled)

the volume of cylinder is half of its total surface area(given)

volume of cylinder = 1/2×44

=22

=22cucm

Answer 2

Answer :

• The volume of cylinder is 1437.34 cm³.

Given:

• The volume of a cylinder is half of its total surface area. If the radius of its base is 7 cm.

To Find :

• The volume of cylinder ?

Solution :

• The volume of cylinder be x.

Step 1,

• Radius of cylinder (r) = 7 cm
• Volume of cylinder (V) = πr²h
• Total surface area of cylinder (TSA) = 2πr(h + r)

Step 2,

• The volume of cylinder is half of its total surface area.

i.e., 1/2 × Volume of cylinder (V) = Total surface area of cylinder (TSA)

➛ 1/2 × πr²h = 2πr(h + r)

➛ πr²h/πr = 2[2(h + r)]

➛ rh = 4(h + r)

➛ rh = 4h + 4r

• r = 7 cm,

So,

➛ 7h = 4h + 4(7)

➛ 7h = 4h + 28

➛ 7h - 4h = 28

➛ 3h = 28

➛ h = 28/3

• Height of cylinder is = 28/3 cm.

Step 3,

• The volume of cylinder is πr²h.

i.e., Volume of cylinder is (V) = πr²h

➛ 22/7(7)²(28/3)

➛ 22/7 × 7 × 7 × 28/3

➛ 22 × 7 × 9.34

➛ 154 × 9.34

➛ 1437.34 cm³

Hence,

• The volume of cylinder is 1437.34 cm³.