Question

what is the formula to find the volume of a pyramid with a rectangular base 10 cm by 5 cm and height 15 cm?
a. $v = 10 \times 5 \times 15$
b. $v = \frac{1}{4} \times 10 \times 5 \times 15$
c. $v = \frac{1}{3} \times 10 \times 5 \times 15$
d. $v = 10 + 5 + 15$
what is the correct formula to calculate the volume of a pyramid with a rectangular base?
a. $v = \frac{1}{2} lh$
b. $v = l \cdot w$
c. $v = \frac{lwh}{3}$
d. $v = bh$
what is the volume of a pyramid with a square base of side 5 cm and height 12 cm?
a. $150 \text{ cm}^3$
b. $100 \text{ cm}^3$
c. $\frac{125}{4} \text{ cm}^3$
d. $200 \text{ cm}^3$
a triangular pyramid has a base area of 30 square units and a height of 15 units. what is its volume?
a. 225 cubic units
b. 450 cubic units
c. 200 cubic units
d. 150 cubic units

Explanation:

Step1: Recall pyramid volume formula

The volume of any pyramid is $V = \frac{1}{3}Bh$, where $B$ is the base area, $h$ is height.
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First Question

Step1: Calculate base area

Base area $B = 10 \times 5$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 10 \times 5 \times 15$

Second Question

Step1: Match general pyramid formula

For rectangular base, $B = l \times w$, so $V = \frac{1}{3}Bh$

Third Question

Step1: Calculate square base area

$B = 5 \times 5 = 25$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 25 \times 12 = 100$

Fourth Question

Step1: Substitute given values into formula

$V = \frac{1}{3} \times 30 \times 15 = 150$

Answer:

1. c. $V = \frac{1}{3} \times 10 \times 5 \times 15$
2. c. $V = \frac{Bh}{3}$
3. b. $100\ \text{cm}^3$
4. (Assuming option d is 150 cubic units) d. 150 cubic units