# Word Problem Involving the Volume of a Triangular Prism Online Quiz

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**Q 1 - A right prism base is a triangle whose sides are 6 cm, 8 cm and 10 cm . Find the volume of the prism if its height is 18 cm.**

### Answer : A

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 6 × 8

= 24 square cm

height h = 18 cm

**Step 2:**

Volume of triangular prism V = Ah = 24(18)

= 432 cu cm

**Q 2 - The base of a right prism is a right triangle with legs 9 and 12 cm. If the volume of the prism be 324 cu cm, find the height of the prism.**

### Answer : C

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 9 × 12

= 54 square cm

Volume V = 324 cu cm

**Step 2:**

Height of triangular prism h = V/A = 324/54

= 6 cm

**Q 3 - The base of a right prism is a triangle with base 12 cm and height 8 cm. Find the volume of the prism if its height is 7 cm.**

### Answer : B

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 12 × 8

= 48 square cm

height h = 7 cm

**Step 2:**

Volume of triangular prism V = Ah = 48(7)

= 336 cu cm

**Q 4 - The base of a right prism is a right triangle with legs 12 and 5 cm. If the volume of the prism be 390 cu cm, find the height of the prism.**

### Answer : D

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 12 × 5

= 30 sq cm

Volume V = 390 cu cm

**Step 2:**

Height of triangular prism h = V/A = 390/30

= 13 cm

**Q 5 - The height of a right prism is 15 cm. and its base is a triangle. If the volume of the prism is 180 cu cm, find the area of the base triangle.**

### Answer : B

### Explanation

**Step 1:**

Height of prism h = 15 cm

Volume V = 180 cu cm

**Step 2:**

Area of base of triangular prism A = V/h = 180/15

= 12 square cm

**Q 6 - A right prism base is a triangle whose sides are 18 cm, 20 cm and 34 cm. Find the volume of the prism if its height is 9 cm.**

### Answer : C

### Explanation

**Step 1:**

Area of base A = $\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{36(36-18)(36-20)(36-34)}$

= 144 square cm

height h = 9 cm

**Step 2:**

Volume of triangular prism V = Ah = 144(9)

= 1296 cu cm

**Q 7 - The height of a triangular prism is 8 cm. and its base is an equilateral triangle of side 4 cm. Find the volume of the prism.**

### Answer : D

### Explanation

**Step 1:**

Area of base A = $a^2\sqrt{3}/4$

= $4^2 \sqrt{3}/4$

= 6.92 square cm

height h = 8 cm

**Step 2:**

Volume of triangular prism V = Ah = 6.92(8)

= 55.36 cu cm

**Q 8 - The height of a right prism is 10 cm and its base is a triangle with 9 cm as base and height 5 cm. Find the volume of the prism.**

### Answer : A

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 9 × 5

= 22.5 square cm

height h = 10 cm

**Step 2:**

Volume of triangular prism V = Ah = 22.5(10)

= 225 cu cm

**Q 9 - The base of a right prism is a triangle with base 12 cm and height 6 cm. Find the volume of the prism if its height is 7 cm.**

### Answer : C

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 12 × 6

= 36 square cm

height h = 7 cm

**Step 2:**

Volume of triangular prism V = Ah = 36(7)

= 252 cu cm

**Q 10 - A right prism stands on a base which is a right triangle with legs 3 cm and 4 cm. Find the volume of the prism if its height is 12 cm.**

### Answer : B

### Explanation

**Step 1:**

Area base A = $\frac{1}{2}$ × 3 × 4

= 6 square cm

height h = 12 cm

**Step 2:**

Volume of triangular prism V = Ah = 12(6)

= 72 cu cm