Question

A circus tent is cylindrical up to a height of 3 m and conical above it. If the diameter of the base is 105 m and the slant height of the conical part is 53 m, then the total canvas used in making the
tent
A) 3597m.
B) 9735m?
C) 3090m2
D) 96.34m?​

Answer 1

Given :-

• Height of Circular tent = 3m

• Diameter of the base = 105m

• Slant height of the Conical Part = 53m

To Find:-

• The Total Canvas used in making the tent.

Formulae used :-

• C.S.A of cone = πrl

• C.S.A of cylinder = 2πrh

Now,

→ Height of Cylinder = 3m

→ Radius of Cylinder = 105/2m

→ Curved surface area of Cylinder = 2πrh

→ 2 × 22/7 × 105/2 × 3

→ 22/7 × 105 × 3

→ 22 × 15 × 3

→ 990m²

Now,

→ Radius of the base of Cone = 105/2

→ Slant height = 53

→ Curved surface area of cone = πrl

→ 22/7 × 105/2 × 53

→ 11 × 15 × 53

→ 8745m²

Therefore, ATQ

→ Total Canvas required = CSA of Cone + CSA of Cylinder

→ Total canvas required = 8745m² + 990m²

→ Total Canvas required = 9375m²

Hence, Total canvas used in making the tent is 9375m²

Therefore, option B is correct.

Answer 2

Given Info :-

• A circus tent is cylindrical up to height = 3 m.

• Diameter of the base = 105 m.

• The slant height of the conical part = 53 m.

To Find :-

• The Total Canvas used in making the tent.

Formulae used :-

• C.S.A (Curved Surface Area) of a Cylinder of Radius "R" and height "h" = 2πRh

• C.S.A (Curved surface area) of a cone = πrl where r is the radius of the cone and l is the slant height.

• Total Canvas used in making the tent = 2πrh + πrl.

Solution :-

★ Radius of the cylindrical part ,

➙ Diameter/2

➙ 105/2 m.

★ Radius of the conical part ,

➙ Diameter/2

Diameter/2➙ 105/2 m.

Hence, amount of Canvas used to make the tent = 2πrh + πrl.

★ 2×22/7×105/2×3+22/7×105/2×53

☯Multiply 2 and 22 to get 44.

➙44/7×105/2×3+22/7×105/2×53

☯Express 44/7× 105 as a single fraction.

➙44×105/7/2×3+22/7×105/2×53

☯Multiply 44 and 105 to get 4620.

➙4620/7/2×3+22/7×105/2×53

☯Divide 4620 by 7 to get 660.

➙660/2×3+22/7×105/2×53

☯Divide 660 by 2 to get 330.

➙330×3+22/7×105/2×53

☯Multiply 330 and 3 to get 990.

➙990+22/7×105/2×53

☯Express 22/7 × 105 as a single fraction.

➙990+22×105/7/2×53

☯Multiply 22 and 105 to get 2310.

➙990+2310/7/2×53

☯Divide 2310 by 7 to get 330.

➙990+330/2×53

☯Divide 330 by 2 to get 165.

➙990+165×53

☯Multiply 165 and 53 to get 8745.

➙990+8745

☯Add 990 and 8745 to get 9735.

★ 9735.

★ Hence, amount of Canvas used to make the tent = 9735 m²

Therefore , Option B is correct.

★ Hope it helps u ★