Mensuration Quiz: 2D and 3D Shapes Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. A rectangle has a perimeter of 46 m and a length of 15 m. What is its area?

   • 120 sq m
   • 112 sq m
   • 135 sq m
   • 104 sq m

   Answer: 120 sq m. l + b = 23, so breadth = 8 m and area = 15 × 8 = 120 sq m.

2. The circumference of a circle is 88 cm. What is its area? (Take pi = 22/7.)

   • 154 sq cm
   • 308 sq cm
   • 616 sq cm
   • 1,232 sq cm

   Answer: 616 sq cm. 2 × 22/7 × r = 88 gives r = 14 cm. Area = 22/7 × 14 × 14 = 616 sq cm.

3. What is the area of a triangle with sides 13 cm, 14 cm and 15 cm?

   • 96 sq cm
   • 72 sq cm
   • 91 sq cm
   • 84 sq cm

   Answer: 84 sq cm. Heron: s = 21; area = sqrt(21 × 8 × 7 × 6) = sqrt(7056) = 84 sq cm.

4. What is the area of an equilateral triangle of side 8 cm?

   • 8 sqrt(3) sq cm
   • 16 sqrt(3) sq cm
   • 32 sqrt(3) sq cm
   • 64 sqrt(3) sq cm

   Answer: 16 sqrt(3) sq cm. Area = sqrt(3)/4 × a² = sqrt(3)/4 × 64 = 16 sqrt(3) sq cm (about 27.7).

5. The total surface area of a cube is 486 sq cm. What is its volume?

   • 729 cu cm
   • 512 cu cm
   • 1,000 cu cm
   • 343 cu cm

   Answer: 729 cu cm. 6a² = 486 gives a² = 81, a = 9 cm. Volume = 9³ = 729 cu cm.

6. What is the volume of a cylinder with radius 7 cm and height 10 cm? (Take pi = 22/7.)

   • 1,450 cu cm
   • 3,080 cu cm
   • 770 cu cm
   • 1,540 cu cm

   Answer: 1,540 cu cm. V = pi r² h = 22/7 × 49 × 10 = 1,540 cu cm.

7. A cone has base radius 6 cm and height 8 cm. What is its curved surface area?

   • 48 pi sq cm
   • 60 pi sq cm
   • 96 pi sq cm
   • 80 pi sq cm

   Answer: 60 pi sq cm. Slant height l = sqrt(6² + 8²) = 10 cm. Curved surface = pi r l = 60 pi sq cm.

8. If the radius of a sphere is doubled, its volume becomes how many times the original?

   • 2 times
   • 4 times
   • 6 times
   • 8 times

   Answer: 8 times. Volume varies as r³, so doubling r multiplies the volume by 2³ = 8. (The surface area becomes 4 times.)

9. A metal sphere of radius 6 cm is melted and recast into a cylinder of radius 4 cm. What is the height of the cylinder?

   • 12 cm
   • 16 cm
   • 18 cm
   • 24 cm

   Answer: 18 cm. Volume is unchanged: 4/3 pi × 216 = pi × 16 × h, so 288 = 16h and h = 18 cm.

10. A rectangular park 40 m by 30 m has a path 2 m wide running all round it on the outside. What is the area of the path?

    • 280 sq m
    • 296 sq m
    • 304 sq m
    • 276 sq m

    Answer: 296 sq m. Outer rectangle = 44 × 34 = 1,496 sq m; minus the park 1,200 gives 296 sq m. Shortcut: 2w(l + b + 2w) = 4 × 74.