Of course! Let's solve each problem step by step. The worksheet asks for the
volume of various pyramids and cones. The general formulas are:
-
Volume of a Pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
-
Volume of a Cone:
\[ V = \frac{1}{3} \pi r^2 h \]
(where \( r \) is the radius, and \( h \) is the height)
---
Problem 1: Square Pyramid
- Base side = 25
- Height = 10
Base Area = \( 25 \times 25 = 625 \)
\[
V = \frac{1}{3} \times 625 \times 10 = \frac{6250}{3}
\]
✔ Answer: \(\boxed{\dfrac{6250}{3}}\)
---
Problem 2: Cone
- Radius = 11
- Height = 21
\[
V = \frac{1}{3} \pi (11)^2 (21) = \frac{1}{3} \pi (121)(21)
\]
\[
= \frac{1}{3} \pi (2541) = 847\pi
\]
✔ Answer: \(\boxed{847\pi}\)
---
Problem 3: Rectangular Pyramid
- Base dimensions: 32 × 14
- Height = 60
Base Area = \( 32 \times 14 = 448 \)
\[
V = \frac{1}{3} \times 448 \times 60 = \frac{26880}{3} = 8960
\]
✔ Answer: \(\boxed{8960}\)
---
Problem 4: Square Pyramid
- Base side = 5 m
- Height = 4 m
Base Area = \( 5 \times 5 = 25 \)
\[
V = \frac{1}{3} \times 25 \times 4 = \frac{100}{3}
\]
✔ Answer: \(\boxed{\dfrac{100}{3}}\)
---
Problem 5: Cone
- Diameter = 4 mm → Radius = 2 mm
- Height = 8 mm
\[
V = \frac{1}{3} \pi (2)^2 (8) = \frac{1}{3} \pi (4)(8) = \frac{32}{3} \pi
\]
✔ Answer: \(\boxed{\dfrac{32\pi}{3}}\)
---
Problem 6: Cone
- Radius = 9 in
- Height = 15 in
\[
V = \frac{1}{3} \pi (9)^2 (15) = \frac{1}{3} \pi (81)(15) = \frac{1}{3} \pi (1215) = 405\pi
\]
✔ Answer: \(\boxed{405\pi}\)
---
Problem 7: Square-based Pyramid
- Side = 9 in
- Height = 12 in
Base Area = \( 9 \times 9 = 81 \)
\[
V = \frac{1}{3} \times 81 \times 12 = \frac{972}{3} = 324
\]
✔ Answer: \(\boxed{324}\)
---
Problem 8: Cone
- Radius = 8 cm
- Height = 15 cm
\[
V = \frac{1}{3} \pi (8)^2 (15) = \frac{1}{3} \pi (64)(15) = \frac{1}{3} \pi (960) = 320\pi
\]
✔ Answer: \(\boxed{320\pi}\)
---
Problem 9: Triangular Pyramid
- Base Area = 15 m²
- Height = 20 m
\[
V = \frac{1}{3} \times 15 \times 20 = \frac{300}{3} = 100
\]
✔ Answer: \(\boxed{100}\)
---
##
✔ Final Answers Summary:
1. \(\boxed{\dfrac{6250}{3}}\)
2. \(\boxed{847\pi}\)
3. \(\boxed{8960}\)
4. \(\boxed{\dfrac{100}{3}}\)
5. \(\boxed{\dfrac{32\pi}{3}}\)
6. \(\boxed{405\pi}\)
7. \(\boxed{324}\)
8. \(\boxed{320\pi}\)
9. \(\boxed{100}\)
All answers are exact as requested. Let me know if you need any step explained further!
Parent Tip: Review the logic above to help your child master the concept of volume of pyramid worksheet.
