Question

A bucket open at the top has top and bottom radii of circular ends as 40 cm and 20 cm respectively. Find the volume of the bucket if its depth
is 21 cm. Also find the area of the tin sheet required for making the bucket. (Use pi =22/7 )​

Answer 1

Answer: Please look at the attachment.

Step-by-step explanation:

The bucket is clearly in the shape of a frustum so we find the volume and surface area using the formulas of frustum.

Answer 2

Recall:

• $\text{Volume of a conical frustum}= \dfrac{1}{3} \pi h ((r_1)^2 + (r_2)^2 + (r_1 \times r_2))$
• $\text{Slanted Height } = \sqrt{(r_1 - r_2)^2 + h^2}$
• $\text {Lateral Surface Area} = \pi (r_1 + r_2) \times s$
• $\text {Area of a circle } = \pi r^2$

Find the volume of the bucket:

$\text{Volume of a conical frustum}= \dfrac{1}{3} \pi h ((r_1)^2 + (r_2)^2 + (r_1 \times r_2))$

$\text{Volume of the bucket}= \dfrac{1}{3} (\dfrac{22}{7}) (21) ((40)^2 + (20)^2 + (40 \times 20))$

$\text{Volume of the bucket}= 61600 \text{ cm}^3$

Find the slanted height of the bucket:

$\text{Slanted Height } = \sqrt{(r_1 - r_2)^2 + h^2}$

$\text{Slanted Height } = \sqrt{40 - 20)^2 + (21)^2}$

$\text{Slanted Height } = 29 \text { cm}$

Find the Lateral Surface Area of the bucket:

$\text {Lateral Surface Area} = \pi (r_1 + r_2) \times s$

$\text {Lateral Surface Area} = \dfrac{22}{7} (40 + 20) \times 29$

$\text {Lateral Surface Area} = 5468.57 \text{ cm}^2$

Find the area of the circle at the bottom of the bucket:

$\text {Area of a circle } = \pi r^2$

$\text {Area of the circle } = \dfrac{22}{7} \times (20)^2$

$\text {Area of the circle } = 1257.14 \text{ cm}^2$

Find the total tin sheet required:

$\text{Tin Sheet required } = 5468.57 + 1257.14$

$\text{Tin Sheet required } = 6725.71 \text{ cm}^2$

Answer: Volume = 61600 cm³, Area of the Tin Sheet= 6725.71 cm²