Q. 84 ΔDEF and ΔGHI are similar triangles. Length of DE is 4 cm and length of the corresponding side GH is 9 cm. What is the ratio of areas of ΔDEF and ΔDEF?

Q. 86 A cylindrical vessel of radius 6 cm is partially ﬁlled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

Q. 87 What is the total surface area (in sq cm) of a hollow cylinder open at both ends, if its length is 22 cm, external radius is 7 cm and thickness is 1 cm? (Take π = 22/7)

Q. 88 If a cylinder of radius 4.3 cm and height 4.8 cm is melted and constructed into a cone of the same radius, what will be the height of this cone? (Use π =22/7)

Q. 90 The perimeters of a square and an equilateral triangle are equal. If the diagonal of the square is 9 cm, what is the area of the equilateral triangle?

(A) 18√3 sq cm (B) 9√3 sq cm (C) 18√2 sq cm (D) 9√2 sq cm

Q. 92 A circular swimming pool is surrounded by a concrete wall 4m wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius (in m) of the pool is

Answer: (B) 20 Explanation: Radius of the swimming pool = R(say) Radius of the pool with the wall = (R + 4) π[(R + 4)² – R²] = (11/25)*π*R²

Q. 93 A cylindrical capsule has hemispherical ends of the radii equal to radius of the cylindrical part. If length of the capsule is 40 m and radius 6 m, what is the total surface area of this capsule?

(A) 3017.14 m² (B) 4525.71 m² (C) 1508.57 m² (D) 754.29 m²

Q. 94 A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

Q. 95 A cylindrical vessel of height 9 cm and radius 7 cm is completely ﬁlled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?

(A) 26.46 cm (B) 39.69 cm (C) 13.23 cm (D) 52.92 cm

Q. 98 Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the endpoints of these two sides is 29 cms. The area of the parallelogram (in sq. cms) is

Q. 100 The diameter of a sphere is twice the diameter of another sphere. The curved surface area of the first and the volume of the second are numerically equal. The numerical value of the radius of the first sphere is