IMO Practice Test: Surface Area & Nets | Class 6 Mathematics

Question 1 of 6 hard

A rectangular prism has SA=148 cm², l=6 cm, w=4 cm. Find h.

2 cm

3 cm

4 cm

5 cm

Explanation: 2(24+6h+4h)=148 → 2(24+10h)=148 → 24+10h=74 → 10h=50 → h=5. Wait: 2(24+10×5)=2×74=148 ✓ h=5 → answer D

Question 2 of 6 hard

A cube's SA is 384 cm². Find volume.

512 cm³

256 cm³

64 cm³

128 cm³

Explanation: 6s²=384, s²=64, s=8, V=8³=512

Question 3 of 6 hard

Two cubes (side 4 cm each) glued face-to-face. Total SA?

144 cm²

160 cm²

128 cm²

192 cm²

Explanation: Each cube SA=6×16=96. Glued: subtract 2 faces → 96+96-2×16=192-32=160 cm²

Question 4 of 6 hard

A rectangular prism has dimensions in ratio 1:2:3 and SA=88 cm². Find volume.

24 cm³

48 cm³

96 cm³

192 cm³

Explanation: Sides x,2x,3x. SA=2(2x²+3x²+6x²)=22x²=88 → x²=4, x=2. Sides: 2,4,6. V=2×4×6=48 cm³

Question 5 of 6 hard

Net of a cylinder (not covered)

2 circles+rectangle

2 circles+square

1 circle+rectangle

2 rectangles

Explanation: Cylinder net = 2 circles + 1 rectangle

Question 6 of 6 hard

A triangular prism has SA=216 cm². Triangle base 6 cm, height 4 cm, equal sides 5 cm. Find prism length.

8 cm

10 cm

12 cm

14 cm

Explanation: Two triangles=2×12=24. Rectangles: 6L+5L+5L=16L. 24+16L=216 → 16L=192 → L=12 cm

IMO Practice Test — Surface Area & Nets